Question 1

A box is of 10 cm long, 8 cm broad and 5 cm high. What is the longest possible length of a pencil that can be put in?

Accepted Answer

Since, the box is in the form of a cuboid. ∴ Required length = √102 +82 + 52 cm = √189 = √9 x 21 = 3√21 cm

Question 2

What is the maximum number of pieces of 5cm x 5cm x 10 cm of cake that can be cut from a big cake of 5 cm x 30 cm x 30 cm size?

Accepted Answer

Maximum number of pieces that can be cut out = (Volume of cake) / (Volume of Each piece of cake) = (5 x 30 x 30)/(5 x 5 x 10) = 18

Question 3

Find the height of the cylinder whose volume is 551 m 3 and the area of the base is 36.5 m 2.?

Accepted Answer

Volume of cylinder = πr2= Area base x height 551 = 36.5 x h h = 511/365 = 14 m

Question 4

The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is?

Accepted Answer

Length of longer rod = √l2 + b2 + h2 = √122 + 92 + 82 = √144 + 81 + 64 = √289 = 17 m

Question 5

The length of longest rod that can fit in a cubical vessel of side 10 cm, is?

Accepted Answer

Longest rod = √(10)2 + (10)2 + (10)2 cm =√300 cm =10√3 cm

Question 6

The length of longest rod that can be placed in a room 20 m long, 16 m broad and 12 m high, is?

Accepted Answer

Length of the rod = √(20)2 + (16)2 + (12)2 m = √800 m = 20√2 m = (20 x 1.41) m = 28.2 m

Question 7

Half cubic meter of gold sheet is extended by hammering so as to cover an area of hectare. The thickness of the sheet is?

Accepted Answer

Thickness = Volume / Area = (1/2)/10000 m = (1 x 100)/(2 x 10000) cm = 0.005 cm

Question 8

In a shower, 5 cm of rain falls. The volume of water that falls on 2 hectare of ground, is?

Accepted Answer

Volume = Area x Thickness of rainfall = 2 x 10000 x (5/100) m3 = 1000 m3

Question 9

The area of the base of a rectangular tank is 6500 sq. cm and the volume of water contained in it is 2.6 cubic meters. The depth of water is?

Accepted Answer

Let depth = D cm. Then, D x 6500 = 2.6 x 100 x 100 x 100 ∴ D = (2.6 x 100 x 100 x 100) / 6500 cm = 400 cm = 4 cm

Question 10

The number of small cubes with edges of 10 cm that can be accommodated in a cubical box 1 meter edge is?

Accepted Answer

Number of cubes = (100 x 100 x 100)/(10 x 10 x 10) = 1000

Question 11

If the volume and surface are of a sphere are numerically the same then its radius is?

Accepted Answer

4/3 πr3 = 4πr2 ⇒ r = 3 units.

Question 12

The volume of a sphere is 88/21 x (14) 3 cm 3. The curved surface of this sphere is?

Accepted Answer

∵ (4/3) x (22/7) x r3 = (88/21) x (14)3 ⇒ r = 14 ∴ Curved surface = 4 x (22/7) x 14 x 14 cm2 = 2464 cm2

Question 13

A cylinder and a cone have the same height and same radius of the base. The ratio between the volumes of the cylinder and the cone is?

Accepted Answer

Ratio of their volumes = [πr2h] / [(1/3)πr2h] = 3/1 = 3 : 1

Question 14

The side of a cube measures 9 cm. What will be the diagonal of the cube (in cm)?

Accepted Answer

Given, side of cube, a = 9 ∴ Diagonal of cube = a√3 = 9√3

Question 15

What will be the surface area of the sphere having 4 cm radius?

Accepted Answer

Required surface area = 4πr2 = 4 x π x 42 = 664π sq cm

Question 16

A hemisphere has 3 cm radius. Calculate its volume.?

Accepted Answer

volume = (2/3)πr3 = (2/3) x π x 33 = (2/3) x π x 27 = 18π cm3

Question 17

Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a square of side 4 cm (in cm 2)?

Accepted Answer

Total surface area of the pyramid = [1/2(perimeter of the base) (Slant height) ] + Area of the base = 1/2 (4) (4) (8) + 42 = 80 cm2

Question 18

A sphere of radius r has the same volume as that of a cone with circular base of radius r. Find the height of the cone.?

Accepted Answer

Given that, Volume of sphere = Volume of cone ⇒ (4/3)πr3 = (1/3)πr2h ⇒ 4r = h

Question 19

A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the rose in level of the field will be?

Accepted Answer

Earth dug out = (3 x 2 x 1.5 ) m3 = 9 m3 Area on which earth has been spread = (22 x 14 - 3 x 2 ) m2 = 302 m2 ∴ Rise in level = Volume/Area = (9/302) m = (9 x 100/302) cm = 2.98 cm

Question 20

Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?

Accepted Answer

Let the volume be x3 and 27x3 ∴ Their edges are x and 3x Now Ratio of their surface area = 6x2 : 54x2 = 1 : 9

Volume and Surface Area Questions