Question 1

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

Accepted Answer

1 dm

Question 2

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

Accepted Answer

Length of longest pole = Length of the diagonal of the room 12 2 + 8 2 + 9 2 = 289 = 17 m

Question 3

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Accepted Answer

1 hectare = 10,000 Sq.m So, Area = (1.5 x 10000) Sq.m Depth = 5/100 m = 1/20 m Therefore, Volume = Area X Depth = 15000 x (1/20)= 750 cu.m

Question 4

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.

Accepted Answer

v 1 v 2 = r 1 2 H r 2 2 H

Question 5

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8g/cu.cm, then the weight of the pipe is

Accepted Answer

External radius = 4 cm Internal radius = 3 cm Volume of iron = 22 7 × 4 2 - 3 2 × 21 c m 3 = 462 c m 3 Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg

Question 6

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface

Accepted Answer

60pi sq.m

Question 7

If radius and height of a cylinder increase by 20% and15% respectively. then what is the % change in curved surface area?

Accepted Answer

% Change in Curved Surface Area is given by % Change in radius + % Change in height + % Change in radius × % Change in height 100 ⇒ + 20 + 15 + 20 × 15 100 = 38 %

Question 8

The curved surface area of a cylindrical pillar is 264 sq.m and its volume is 924 cub.m. Find the ratio of its diameter to its height

Accepted Answer

πr 2 h 2 πr 2 h = 924 264 => r = (24/364) x 2 = 7m 2 πrh = 264 ⇒ h = ( 264 × 7 22 × 1 2 × 1 7 ) = 6 m Required Rato =2r/h =14/6 = 7:3

Question 9

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

Accepted Answer

Number of bricks = volume of the wall/volume of one brick = (800 x 600 x 22.5)/(25 x 11.25 x 6 )= 6400

Question 10

Find the surface area of a10cm x 4cm x 3cm brick

Accepted Answer

surface area = [2(10*4 + 4*3 + 10*3)]sq.cm = 164 sq.cm

Question 11

The circumference of a circular base of Cylinder is 44 cm and its hight is 15 cm. Then the volume of the cylinder is?

Accepted Answer

Given Circumference of a circular base of a cylinder = 44 cm We know that Circumference of a circle = 2 πr = 44 ⇒ r = 22 π Now given the height of a cylinder h = 15 cm Volume of a cylinder V = πr 2 h = π 22 π 2 15 = 22 x 22 x 15 3 . 14 = 2311 cm 3 .

Question 12

A Conical tent was erected by the army at a base camp with height 3 m and base diameter 10 m. If every person requires 3.92 cu.m air, then how many persons can be seated in that tent approximately?

Accepted Answer

Given height of the conical tent = 3 m Diameter = 10 => Radius = D/2 = 10/2 = 5 m Now, as the tent is in the conical form Volume of the conical tent = π r 2 h 3 => (22 x 5 x 5 x 3) / (7 x 3) = 22 x 25/7 = 78.54 cu.m Given each person requires 3.92 cu.m of air => Number of persons can be seated in the tent = 78.54/3.92 = 20.03 =~ 20

Question 13

Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?

Accepted Answer

Volume of the wall = (2400 x 800 x 60) cu.cm Volume of bricks = 90% of the volume of the wall = [(90/100) x 2400 x 800 x 60] cu.cm Volume of 1 brick = (24 x 12 x 8) cu.cm Number of bricks = [(90/100) x (2400 x 800 x 60) ]/ (24 x 12 x 8) = 45000

Question 14

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?

Accepted Answer

4/3 π x 10 x 10 x 10 = 8 x 4/3 π x r x r x r r = 5 4π x 5 x 5 = 100π

Question 15

If the volume of the cube is 729 cm3 , then the surface area of the cube will be

Accepted Answer

volume = a 3 = 729; => a = 9 surface area= 6 a 2 = (6 x 9 x 9) = 486 sq.cm

Question 16

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles ?

Accepted Answer

Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively. 2 πs = 264 and 2 πl = 352 s = 264 2 π and l = 352 2 π Difference between the areas = π l 2 - π s 2 = π 176 2 π 2 - 132 2 π 2 = 1762 π - 1322 π = (176 - 132)(176 + 132) / π = (44 x 308) / (22/7) = 4312 sq.m

Question 17

Ratio between heights of two cylinder in the ratio 3:5. Their volumes are in the ratio 27:80. Find ratio between their radius ?

Accepted Answer

3:4

Question 18

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

Accepted Answer

Volume of block=(6 x 9 x 12) cu.cm = 648 cu.cm Side of largest cube = H.C.F of 6,9,12 = 3cm Volume of the cube=(3 x 3 x 3)=27cu.cm Number of cubes=(648/27)=24

Question 19

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Accepted Answer

Volume of the large cube = 3 3 + 4 3 + 5 3 = 216 cu.cm. Let the edge of the large cube be a. So, a 3 = 216 =>a = 6 cm. Required ratio = 6 3 2 + 4 2 + 5 2 6 6 2 = 25 18

Question 20

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

Accepted Answer

Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] sq.cm = (2 x 434)sq.cm = 868 sq.cm

Volume and Surface Area Questions