SOLID GEOMETRY III

1Diagram 1 shows a right pyramid.

Diagram 1

Given that the volume of the pyramid is 660 cm3, find the height, in cm, of the pyramid. A 6 C 12B 9 D 15

2

Diagram 2 shows a right circular cone.

Diagram 2

Given that the curved surface area of the cone is 260π cm2, find the volume, in cm3, of the cone. A 800π C 3 000πB 1 200π D 4 800π

3 In Diagram 3, ABCD in the shape of a trapezium is the cross-section of a right prism.

Diagram 3

Given that the volume of the prism is 546 cm3, find the value of m, in cm. A 3 C 5B 4 D 6

4 Diagram 4 shows a cylindrical solid. The shaded region in the shape of a right cone is removed.

Diagram 4

The height of the cylinder is 7 cm while the height of the cone is 3 cm. Find the volume, in cm3, of the remaining solid. A 1 147π C 3 441πB 2 294π D 4 588π

5 Diagram 5 shows a right circular cylinder.

Diagram 5

If 80% of the cylinder is filled with water, find the volume, in litres, of the portion of the cylinder which is not filled with water.(Use π = ) A 6.38 C 25.5B 12.75 D 51

6 Diagram 6 shows two right pyramids with the common base ABCD.

Diagram 6

Given that AB = 7 cm, BC = 12 cm and EF = 24 cm. Find the total volume, in cm3, of the pyramids. A 672 C 1 344B 840 D 2 016

7Diagram 7 shows two right cones with the common diameter WX.

Diagram 7

Given that WX = 42 cm and YZ = 18 cm. Find the total volume, in cm3, of the cones.(Use π = ) A 2 772 C 8 316B 4 158 D 11 088

8

Diagram 8 shows a right cylinder and a cuboid.

Diagram 8

If both the cylinder and the cuboid have the same volume, find the value of p, in cm.(Use π = ) A 18 C 26B 22 D 30

9

A right cylinder is filled completely with paint. If the volume of the paint in the cylinder is 3 080 cm2

and the radius of the cylinder is 7 cm, find the height, in cm, of the cylinder.(Use π = ) A 15 C 25B 20 D 30

10

Diagram 10 shows three hemispheres of the same size.

Diagram 10

Find the total volume of three hemispheres, in cm3.(Use π = 3.14) A 785 C 1 044.05B 981.25 D 1 177.5

Answer:

1 C          2 A          3 D          4 A          5 A6 A          7 C          8 B          9 B          10 A