Category: Surface Area Of Solids

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 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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Calculate the surface area of the solid regular hexagonal prism shown below, giving your answer to 3sf. (4mks)

29/4/2023

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Calculate the surface area of the solid regular hexagonal prism shown below, giving your
answer to 3sf. (4mks)

ANSWER

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QUESTION AND ANSWER ON VOLUME AND SURFACE AREA MODEL06012023018

5/1/2023

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The figure below is a cone whose base radius is 3.5cm and slant height 7cm. The net of the cone is a sector of a circle.

21/11/2021

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The figure below is a cone whose base radius is 3.5cm and slant height 7cm. The net of the cone is a sector of a circle.

(a) Find the angle subtended at the centre of the sector. (2mks)

(b) Draw the net of the solid. (1mk)

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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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The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.

24/10/2021

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The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.

a) If a triangle BAF = 30⁰, calculate the surface area of the prism (3mks)

b) Draw a clearly labelled net of the prisms (1mk)

Worked Answer:

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Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm3, find the surface area of the smaller can (3mks)

24/10/2021

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Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm³, find the surface area of the smaller can (3mks)

Worked 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 2005.PP1.QN.12

17/9/2020

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Form 2 Mathematics

A cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length into two equal pieces.

Calculate the surface area of one piece (Take ∏ as ²²/₇ (4mks)

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 2004.PP1.QN.19

12/9/2020

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Form 2 Mathematics

The figure below represents a model of a solid structure in the shape of a frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28cm and slant height of 60cm.

Calculate

a) The area of hemispherical surface.
b) The total surface area of the model.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN23

10/9/2020

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Form 2 Mathematics

The figure below represents a conical flask. The flask consists of a cylindrical part and a frustum of a cone. The diameter of the base is 10cm while that of the neck is 2 cm. the vertical height of the flask is 12cm.

Calculate, correct to 1 decimal place
a) The slant height of the frustum part
b) The slant height of the smaller cone that was cut off to make the frustum part
c) The external surface area of the flask. (Take π =3.142)

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 2013PP1QN24

2/9/2020

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Form 2 Mathematics

The figure below represents a cone of height 12 cm and base radius of 9 cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm.

a) Calculate:
i. The base radius of the conical hole;
ii. The volume, in terms of π, of the smaller cone that was removed.
b) (i) Determine the slant height of the original cone.
(ii) Calculate, in terms of it, the surface area of the remaining solid after the smaller cone is removed.

answers

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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN15

2/9/2020

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Form 2 Mathematics

The figure below represents a pentagonal prism of length 12 cm.The cross-section is a regular pentagon of side 5 cm.

Calculate the surface area of the prism correct to 4 significant figures.

answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN010

2/9/2020

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Form 2 Mathematics

The length of a solid prism is 10cm. Its cross section is an equilateral triangle of side 6cm.
Find the total surface area of the prism.

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN18

31/8/2020

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Form 2 Mathematics

The figure below represents a solid cuboid ABCDEFGH with a rectangular base, AC= 13cm, BC = 5 cm and CH = 15cm.

(a) Determine the length of AB,
(b) Calculate the surface area of the cuboid.
(c) Given that the density of the material used to make the cuboid is 7.6 g/cm3, calculate its mass in kilograms.
(d) Determine the number of such cuboids that can fit exactly in a container measuring 1.5 m by 1.2 m by 1 m.

answers

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K.C.S.E Mathematics Q & A - MODEL 2011PP1QN17

27/8/2020

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Form 2 Mathematics

A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm.
(a) Calculate correct to two decimal places:
(i) the surface area of the solid;
(ii) the volume of the solid
(b) If the density of the material used to make the solid is 1.3 g/cm³, calculate its mass in kilograms.

answers

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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN24

25/8/2020

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Form 2 Mathematics

A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm².
(a) Express in terms of x:
(i) the internal height h, of the box;
(ii) the internal volume V, of the box.
(b) Find:
(i) the value of x for which the volume V is maximum;
(ii) the maximum internal volume of the box.

answers

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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN14

25/8/2020

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Form 2 Mathematics

A cylindrical solid whose radius and height are equal has a surface area of 154 cm². Calculate its diameter, correct to 2 decimal places. (Take π = 3.142)

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN21

20/8/2020

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Form 2 Mathematics

A glass, in the form of a frustum of a cone, is represented by the diagram below.
The glass contains water to a height of 9 cm,. The bottom of the glass is a circle of radius 2 cm while the surface of the water is a circle of radius 6 cm.

a) Calculate the volume of the water in the glass
b) When a spherical marble is submerged into the water in the glass, the water level rises by 1 cm.
Calculate:
i) The volume of the marble;
ii) The radius of the marble

answers

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K.C.S.E Mathematics Q & A - MODEL 2008PP1QN13

16/8/2020

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Form 2 Mathematics

A rectangular and two circular cut-outs of metal sheet of negligible thickness are used to make a closed cylinder. The rectangular cut-out has a height of 18cm. Each circular cu-out has a radius of 5.2cm. Calculate in terms of pi, the surface area of the cylinder

answer

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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN09

12/8/2020

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Form 2 Mathematics

A cylindrical solid of radius 5 cm and length 12 cm floats lengthwise in water to a depth of 2.5 cm as shown in the figure below.

Calculate the area of the curved surface of the solid in contact with water, correct to 4 significant figures

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

​ANSWER

Calculate the surface area of the solid regular hexagonal prism shown below, giving youranswer to 3sf. (4mks)

​ANSWER

​The figure below is a cone whose base radius is 3.5cm and slant height 7cm. The net of the cone is a sector of a circle.

​(a) Find the angle subtended at the centre of the sector. (2mks)

(b) Draw the net of the solid. (1mk)

​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:

​The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.

a) If a triangle BAF = 300, calculate the surface area of the prism (3mks)

b) Draw a clearly labelled net of the prisms (1mk)

Worked Answer:

Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm3, find the surface area of the smaller can (3mks)

Worked Answer:

Form 2 Mathematics

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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

Calculate the surface area of the solid regular hexagonal prism shown below, giving your
answer to 3sf. (4mks)

ANSWER

The figure below is a cone whose base radius is 3.5cm and slant height 7cm. The net of the cone is a sector of a circle.

(a) Find the angle subtended at the centre of the sector. (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)

The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.

a) If a triangle BAF = 30⁰, calculate the surface area of the prism (3mks)

Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm³, find the surface area of the smaller can (3mks)