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)
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
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. Form 1 MathematicsThe 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 cm^{3} Calculate the radius of a solid spherical ball of mass 540 density of 10g per cm^{3}. Form 2 MathematicsThe 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) 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. 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.
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. 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. 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/cm^{3} and that of milk as 1.2 g/cm^{3}, find the mass in grams of 2.5 litres of the mixture. 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 160cm^{3}, find the volume of the frustum.
Form 2 MathematicsForm 2 Mathematics
The density of a substance A is given as 13.6 g/cm^{3} and that of a substance B as 11.3 g/cm^{3}. Determine, correct to one decimal place, the volume of Bthat would have the same mass as 50cm^{3} of A.
Form 2 Mathematics
The volume of a cube is 1728 cm^{3}. Calculate, correct to 2 decimal places, the length of the diagonal of a face of the cube.
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 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. Form 2 Mathematics
The mass of solid cone of radius 14cm and height 18cm is 4.62kg. find its density in g/cm^{3}
Form 2 Mathematics
A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.
Form 2 MathematicsThe length of a hallow cylindrical pipe is 6 metres. Its external diameter is 11cm and has a thickness of 1cm. Calculate the volume in cm^{3} of the material used to make the pipe. Take П as 3.142 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. Form 2 Mathematics
A cylindrical pipe 2 ½ metres long has an internal diameter of 21 millimetres and an external diameter of 35 millimetres. The density of the material that makes the pipe is 1.25 g/cm3.
Calculate the mass of mass of the pipe in kilograms. (Take π = 22/7). Form 2 MathematicsForm 1 Mathematics
The figure VPQR below represents a model of a top of a tower. The horizontal base PQR is an equilateral triangle of side 9cm. The lengths of edges are VP = VQ = VR = 20.5cm. Point M is the mid point of PQ and VM = 20cm. Point N is on the base and vertically below V.
Calculate:
a) i) Length of RM ii) Height of model iii) Volume of the model b) The model is made of material whose density is 2,700 kg/m^{3}. Find the Mass of the model. 
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