Category: Volume And Capacity

A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slanting height of the conical part is 10 cm. (Тake л = 3.142)

22/5/2023

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A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slanting height of the conical part is 10 cm. (Тake л = 3.142).
Calculate the:
(a) height of the solid; (2 marks)
(b) surface area of the solid, correct to 1 decimal place; (4 marks)
(c) volume of the solid, correct to 1 decimal place. (4 marks)

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 18

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The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm.

13/5/2023

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The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm.

a) Calculate the total surface area of the frustum (4mks)
b) Calculate the volume of the solid frustum. (3mks)
c) Calculate the angle between the planes BCHG and the base EFGH. (3mks

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The figure below is a cross-section of a model of a swimming pool of length 30cm.

11/5/2023

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The figure below is a cross-section of a model of a swimming pool of length 30cm.

Find the capacity of the actual pool in liters given that its length is 27m. (4mks)

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The figure below is a right pyramid of rectangular base of length 12cm and width 9cm. The slanting edge has a length of 19.5cm.

29/4/2023

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The figure below is a right pyramid of rectangular base of length 12cm and width 9cm.
The slanting edge has a length of 19.5cm.

ANSWER

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QUESTION AND ANSWER ON VOLUME AND SURFACE AREA MODEL06012023018

5/1/2023

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A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius 7cm is submerged into the cylinder and removed. Find the change in height of water level in the cylinder. (4 marks)

11/12/2022

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A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius 7cm is submerged into the cylinder and removed. Find the change in height of water level in the cylinder. (4 marks)

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From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.

22/11/2021

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From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.

(a) Determine the number of liters of water discharged from reservoir in one hour. (4mks)

(b) The water flows from the reservoir for 18 hours per day for 25 days per month and serves a population of 2500 families. Determine the average consumption of water per family per month giving your answer to the nearest 100 litres. (4mks)

(c) The water is charged at the rate of sh.4.50 per 100 litres. Calculate the average water bill per family per month. (2mks)

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A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water

25/10/2021

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A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water.

a) Calculate the volume of the water. (Take  = 3.142) (6mks)

b) All the water is poured into a cylindrical container of circular radius 12cm. If the cylinder has height 45cm, calculate the surface area of the cylinder which is not in contact with water (4mks)

Worked Solution:

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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN17

22/9/2020

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Form 2 Mathematics

A rectangular water tank measures 2.4 m long, 2 m wide and 1.5 m high. The tank contains some water up to a height of 0.45 m.
(a) Calculate the amount of water, in litres, needed to fill up the tank
(b) An inlet pipe was opened and water let to flow into the tank at a rate of 10 litres per minute.After one hour, a drain pipe was opened and water allowed to flow out of the tank at a rate of 4 litres per minute.
Calculate:
(i) the height of water in the tank after 3 hours;
(ii) the total time taken to fill up the tank.

answers

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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.14

19/9/2020

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Form 1 Mathematics

The density of a solid spherical ball varies directly as its mass and inversely as the cube of its radius.

When the mass of the ball is 500g and the radius is 5 cm, its density is 2 g per cm³ Calculate the radius of a solid spherical ball of mass 540 density of 10g per cm³.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.19

19/9/2020

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Form 2 Mathematics

The diagram below represents a rectangular swimming pool 25m long and 10m wide. The sides of the pool are vertical.

The floor of the pool slants uniformly such that the depth at the shallow end is 1m at the deep end is 2.8 m.

(a) Calculate the volume of water required to completely fill the pool.

(b) Water is allowed into the empty pool at a constant rate through an inlet pipe. It takes 9 hours for the water to just cover the entire floor of the pool.

Calculate:

(i) The volume of the water that just covers the floor of the pool ( 2 marks)

(ii) The time needed to completely fill the remaining of the pool ( 3 marks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN17

18/9/2020

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Form 2 Mathematics

A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.
(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places.
(b) Find the capacity of the tank, in litres, correct to the nearest litre.
(c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water.

answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN03

18/9/2020

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Form 2 Mathematics

The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid.

answer

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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN19

16/9/2020

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Form 2 Mathematics

A solid S is made up of a cylindrical part and a conical part. The height of the solid is 4.5 m.
The common radius of the cylindrical part and the conical part is 0.9 m. The height of the conical part is 1.5 m.
(a). Calculate the volume. correct to 1 decimal place, of solid S.
(b). Calculate the total surface area of solid S.
A square base pillar of side 1.6 m has the same volume as solid S. Determine the height of the pillar, correct to 1 decimal place.

answers

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN20

15/9/2020

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Form 1 Mathematics

A water vendor has a tank of capacity 18 900 litres. The tank is being filled with water from two pipes A and B which are closed immediately when the tank is full. Water flows at the rate of 150 000cm3/minute through pipe A and 120 000 cm3/ minute through pipe B.
(a) If the tank is empty and the two pipes are opened at the same time, calculate the time it takes to fill the tank
(b) On a certain day the vendor opened the two pipes A and B to fill the empty tank. After 25 minutes he opened the outlet tap to supply water to his customers at an average rate of 20 litres per minute.
(i) Calculate the time it took to fill the tank on that day.
(ii) The vendor supplied a total of 542 jerricans, each containing 25 litres of water, on that day. If the water that remained in the tank was 6300 litres,
calculate, in litres, the amount of water that was wasted.

answers

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN14

15/9/2020

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Form 1 Mathematics

Water and milk arc mixed sueh that the volume of water to that of milk is 4:1,
Taking the density of water as 1 g/cm³ and that of milk as 1.2 g/cm³, find the mass in grams of 2.5 litres of the mixture.

answer

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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN14

14/9/2020

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Form 2 Mathematics

A small cone of height 8cm is cut off from a bigger cone to leave a frustum of height 16cm. If. the volume of the smaller cone is 160cm³, find the volume of the frustum.

answer

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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.13

11/9/2020

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Form 2 Mathematics

The figure below represents a hexagon of side 5cm.

Find the volume of the prism.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN06

9/9/2020

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Form 2 Mathematics

The density of a substance A is given as 13.6 g/cm³ and that of a substance B as 11.3 g/cm³. Determine, correct to one decimal place, the volume of Bthat would have the same mass as 50cm³ of A.

answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN03

9/9/2020

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Form 2 Mathematics

The volume of a cube is 1728 cm³. Calculate, correct to 2 decimal places, the length of the diagonal of a face of the cube.

answer

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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN20

7/9/2020

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Form 2 Mathematics

The figure below shows a right pyramid VABCDE. The base ABCDE is regular pentagon. AO = 15cm and VO = 36 cm.

Calculate:
(a) The area of the base correct to 2 decimal places
(b) The length AV
(c) The surface area of the correct to 2decimal places
(d) The volume of the pyramid correct to 4 significant figures

answers

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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN13

7/9/2020

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Form 2 Mathematics

The figure below shows a rectangular container of dimensions 40cm by 25cm by 90cm. a cylindrical pipe of radius 7.5cm is fitted in the container as shown.

Water is poured into the container in the space outside the pipe such that the water level is 80% the height of the container. Calculate the amount of the
water, in litres, in the container in 3 significant figures.

answer

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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN03

7/9/2020

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Form 2 Mathematics

The mass of solid cone of radius 14cm and height 18cm is 4.62kg. find its density in g/cm³

answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN017

3/9/2020

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Form 2 Mathematics

A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.

a) Calculate the volume of milk in the tank in cubic metres.
b) Pyramid on an equilateral triangular base of side 16cm. The height of each packet is 1.6cm. Full packets obtained are sold at sh.25 per packet.
- i) The volume of milk in cubic centimeters, contained in each packet to 2 significant figures
- ii) The exact amount that will be realized from the sale of all the packets of milk.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN013

3/9/2020

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Form 2 Mathematics

The length of a hallow cylindrical pipe is 6 metres. Its external diameter is 11cm and has a thickness of 1cm. Calculate the volume in cm³ of the material used to make the pipe.

Take П as 3.142

Answer

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm.

​The figure below is a cross-section of a model of a swimming pool of length 30cm.

​The figure below is a right pyramid of rectangular base of length 12cm and width 9cm. The slanting edge has a length of 19.5cm.

​ANSWER

​From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.

​(a) Determine the number of liters of water discharged from reservoir in one hour. (4mks)

(b) The water flows from the reservoir for 18 hours per day for 25 days per month and serves a population of 2500 families. Determine the average consumption of water per family per month giving your answer to the nearest 100 litres. (4mks)

(c) The water is charged at the rate of sh.4.50 per 100 litres. Calculate the average water bill per family per month. (2mks)

​A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water.

​a) Calculate the volume of the water. (Take  = 3.142) (6mks)

​b) All the water is poured into a cylindrical container of circular radius 12cm. If the cylinder has height 45cm, calculate the surface area of the cylinder which is not in contact with water (4mks)

Worked Solution:

Form 2 Mathematics

17

Form 1 Mathematics

N.14

Form 2 Mathematics

N.19

Form 2 Mathematics

17

Form 2 Mathematics

3

Form 2 Mathematics

19

Form 1 Mathematics

20

Form 1 Mathematics

14

Form 2 Mathematics

14

Form 2 Mathematics

N.13

Form 2 Mathematics

6

Form 2 Mathematics

3

Form 2 Mathematics

20

Form 2 Mathematics

13

Form 2 Mathematics

3

Form 2 Mathematics

17

Form 2 Mathematics

13

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The figure below is a cross-section of a model of a swimming pool of length 30cm.

The figure below is a right pyramid of rectangular base of length 12cm and width 9cm.
The slanting edge has a length of 19.5cm.

ANSWER

From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.

(a) Determine the number of liters of water discharged from reservoir in one hour. (4mks)

A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water.

a) Calculate the volume of the water. (Take  = 3.142) (6mks)

b) All the water is poured into a cylindrical container of circular radius 12cm. If the cylinder has height 45cm, calculate the surface area of the cylinder which is not in contact with water (4mks)