Maths - Volume and Surface area

Solid Cylinder: let r be the radius and h be height of a solid cylinder, then

(i) curved (lateral) surface area = 2 rh, (ii) total surface area = 2 r(h +r)
(iii) volume = r²h
Cone: Let r, h and l be the radius, height and slant height respectively of a cone, then, (i) slant height = r² +h², (ii) curved (lateral) surface area = rl
(iii) total surface area = r(l +r), (iv) volume = (1/3) r²h
Solid sphere: Let r be the radius of a solid sphere, then
(i) surface area = 4r², (ii) volume = (4/3) r³
Volume of cube: Side x side x side, Surface area= 6 x side x side
Volume of cuboid: L x B x H, Surface area= 2 (LB+LH+BH)
                                               Exercise

1. Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.

        a. 866 b. 868 c. 686 d. 888 e. None

2. Find the length of the longest pole that can be placed in a room 12 mt long, 8 mt board and 9 m high.

        a. 17 b. 71 c. 77 d. 11 e. None

3. The surface area of a cube is 1734 sq cm. Find its volume.

        a. 9134 b. 1349 c. 4913 d. 9933 e. None

4. Three solid cubes of sides 1cm, 6cm & 8cm are melted and formed a new cube. Find the surface area of new cube.

         a. 486 b. 468 c. 684 d. 448 e. None

5. Find the volume, curved surface area and total surface area of a cyclinder with diameter of base 7cm and height 40cm.

         a. 1540, 880, 957 b. 1550, 880, 957 c. 1540, 880, 950 c. Cant find e. None

6. If the capacity of a cyclindrical tank is 1848 cube mt and the diameter of its base is 14 m, than find the debth of the tank is:

         a. 10 b. 11 c. 12 c. 13 e. None

7. How many iron rods, each of length 7 m and diameter 2cm can be made out of 0.88 cubic meter of iron?

        a . 400 b. 4 c. 40 c. 4000 e. None

8. The radii of two cylinders are in ratio 3:5 and their heights are in ratio of 2:3. Find the ratio of their curved surface areas.

         a. 2:5 b. 5:3 c. 3:3 c. Cant find e. None

9. Find the slant hight of a cone of radius 21 cm and hieght 28cm.

         a. 35 b. 53 c. 0.35 d. 0.53 e. None

10. The radii of the bases of a cylinder and a cone are in the ratio of 3 : 4 and their heights are in the ratio of 2 : 3. Find the ration of their volume.

        a. 9 : 8 b. 8 : 9 c. 8 : 8 d. Data inadequate e. None

11. How many spherical bullets can be made out of a lead cyclinder 28 cm high and with base radius 6 cm, each bullet being 1.5cm in diametre?

        a. 1792 b. 1729 c. 1722 d. 1799 e. None

12. A cone and a sphare have equal radii and equal volumes. Find the ratio of the diametre of the sphare to the height of the cone.

        a. 1 : 2 b. 1 : 1 c. 2 : 2 d. 2 : 1 e. None

13. A cone, a hemisphare and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.

       a. 1 : 2 : 3 b. 1 : 2: 2 c. 3 : 2 : 1 d. Cant find e. None

14. The capacity of a tank of dimentions (8 m x 6 m x 2.5 m) is:

        a. 120 lt b. 1200 lt c. 12000 lt d. 120000 lt
Answer: 1b, 2b, 3c, 4a, 5a, 6c, 7a, 8a, 9a, 10a, 11a, 12a, 13a, 14d