Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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

Question 16

There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes

Accepted Answer

R =OA = OB = Radius of hemisphere. = Radius of cylinder ABCD. Height of the cylinder = BC = radius Volume of cylinder/Volume of hemisphere = πr 3 2 3 πr 3

Question 17

The capacity of a tank of dimensions (8m x 6m x 2.5m)is

Accepted Answer

capacity of a tank = volume of tank = [ (8 x 100) x (6 x 100) x (2.5 x 100) ]/ 1000 litres = 120000 litres

Question 18

How many iron rods, each of length 7 mts and diameter 2 cms can be made out of 0.88 cubic metre of iron ?

Accepted Answer

Given length of iron rod =7 mts and and diameter of rod = 2 cms => r = 1/100 mts Therefore, Volume of one rod = πr 2 h cu. m = 22 7 × 1 100 2 × 7 cu. m = 11 5000 cu. m Given volume of iron = 0.88 cu. m Therefore, Number of rods = 0 . 88 × 5000 11 = 400.

Question 19

The areas of three consecutive faces of a cuboid are 12 cm², 20cm² and 15 cm², then the volume (in cm³) of the cuboid is

Accepted Answer

From the given data, let the length, breadth and height of the cuboid are m, n, r m x n = 12 n x r = 20 r x m = 15 Hence, m x n x n x r x r x m = 12 x 20 x 15 mnr = sqrt of (12x20x15) = 60 cub.cm.

Question 20

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:

Accepted Answer

60 kg

Volume and Surface Area Questions