calculate the volumes of a prism, cone and sphere
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1 VOLUMES OF SOLIDS By the end of this set of exercises, you should be able to calculate the volumes of a prism, cone and sphere Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 13
2 VOLUMES OF SOLIDS A. Volume of a Prism Volume prism = Area base x height Exercise 1 1. For each of the following prisms, the area of the base or end face is given. Calculate the volumes of the prisms: Area = 29 cm 2 Area = 8 cm 2 (b) Area = 12 5 cm 2 (c) 8 cm (d) (e) (f) Area = 52 mm 2 Area = 15 4 cm cm 11 mm Area = 9 2 cm 2 2. This time you must calculate the shaded area first, then find the volumes of the prisms. (b) (c) 7 5 cm 4 cm 5 cm rectangle right angled triangle (d) (e) (f) 20 cm 7 5 cm square 12 cm height = 1 12 cm isosceles triangle square with square hole circle with radius = Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 14
3 3. The cylinder a special prism. Calculate the volumes of the following cylinders: 8 cm (b) 3 cm (c) Volume (cylinder) = πr2h 9 5 cm 2 5 cm 13 cm (d) (e) 6 5 cm 2 cm 1 metre 4. Remember: 1 cm 3 = 1 ml ; 1000 cm 3 = 1000 ml = 1 litre How many litres of water will the following drums hold? 25 cm (b) (c) 60 cm 35 cm 55 cm 5. A cylindrical tin of Maxcafe Coffee is 10 centimetres high and has a base diameter of 7 centimetres. What is the volume of coffee in the tin when it is full? Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 15
4 6. This rectangular storage tank is full of white paint. Calculate the volume of paint in the tank in cubic centimetres (cm 3 ). (b) Calculate the volume of this cylindrical paint tin. 50 cm 20 cm 45 cm 1 (c) How many times can the paint tin be completely filled from the tank? 80 cm 7. Meanz Beanz tins are packed into this cardboard box. How many tins can be placed on the bottom layer? 8 cm M B 33 cm (b) How many layers will there be? (c) How many tins can be packed in the box altogether? (d) How much air space in the box is there around all the tins? 32 cm 48 cm 8. This cast iron pipe has an internal diameter of 16 centimetres and an outside diameter of 20 centimetres. The pipe is 1 5 metres long cm 1 5 m Calculate the volume of iron needed to make the pipe. 9. How much liquid feeding will this semi-cylindrical pig-trough hold? 120 cm Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 16
5 B. Volume of a Cone Exercise 2 Volume (cone) = 1 / 3 πr2h 1. Calculate the volumes of the following conical shapes: (b) (c) (d) (e) 3 5 cm cm The wafer of an ice-cream cone has a diameter of 6 centimetres. The cone is 10 centimetres high. Calculate the volume of the cone. 3. The sloping height of this cone is 2. The base radius is. 2 (b) Calculate the height of the cone. Calculate the volume of the cone. Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 17
6 4. Calculate the total volumes of the following shapes. (b) 25 cm 20 cm 5. Water is poured into this conical flask at the rate of 50 millilitres per second. 12 cm Calculate the volume of the flask. (b) How long will it take, to the nearest second, to fill the flask to the top? 24 cm Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 18
7 C. Volume of a Sphere Exercise 3 1. Calculate the volumes of the following spheres: (b) (c) Volume (sphere) = 4 / 3 πr3 6 5 cm 9 2 cm (d) (e) 10 4 cm 2. This football is fully inflated. Calculate the volume of air inside the football. 24 cm 3. Calculate the volumes of these two hemispheres : (b) 14 cm 8 5 cm Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 19
8 4. Calculate the volume of water which can be stored in this copper hot water tank in cm 3. The tank consists of a cylinder with two hemispherical ends. (b) How many litres of water will it hold? (1cm 3 = 1 ml; 1000 ml = 1 litre). 60 cm 5. Calculate the volume of this child s rocking toy which consists of a cone on top of a hemisphere. 6. This decorative wooden fruit bowl is in the shape of a hollowed out hemisphere. 1 Calculate the volume of wood required to make it. Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 20
9 Checkup for Volumes of Solids 1. Calculate the volumes of the following prisms: Area = 12 5 cm 2 (b) Area = 28 cm 2 (c) 9 cm Area = 18 5 cm 2 2. Calculate the shaded areas and use them to find the volume of each shape. 9 cm (b) 22 cm (c) 12 cm 3. Calculate the volumes of the following shapes: right angled triangle 9 cm 8 5 cm height = 13 cm (b) isosceles triangle 8 cm 8 cm Vol (cylinder) = πr 2 h Vol (cone) = 1 / 3 πr 2 h Vol (sphere) = 4 / 3 πr 3 (c) 10 4 cm 4. This shape consists of a cone, a cylinder and a hemisphere. Calculate its total volume. 12 cm Mathematics Support Materials: Mathematics 1 (Int 2) Student Materials 21
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