SOLID GEOMETRY

Formula Sheet

Volume of Solid Geomety

1. Cylinder, V = πr2h

2. Prism, V = Ah (A is area of base)

3. Pyramid, V = 13 Ah

4. Cone, V = 13 πr2h

5. Sphere, V = 43 πr3

6. Hemisphere, V = 23 πr3

7. Area of Trapezium, = 12 X sum of parallel sides X height

8. Circumference of = 2πr

Circle

9. Area of Circle, = πr2

SPM 2005

Diagram below shows a solid cone with radius 9cm and height 14 cm. A cylinder with radius 3cm and height 7cm is taken out of the solid.

Calculate the Volume, in cm3, of the remaining solid.

[Use π = 227 ] [4 marks]

Answer :

Volume of Remaining Solid = Volume of Cone – Volume of Cylinder

= [ 13 πr2h ] – [ πr2h ]

= [( 13)( 227

)(9)2(14) ] – [( 227

)(3)2(7) ] = 1188 – 198

= 990 cm 3