Utilizing ICSE S Chand Maths Class 9 Solutions Chapter 18 Surface Area and Volume of 3D Solids Chapter Test as a study aid can enhance exam preparation.

## S Chand Class 9 ICSE Maths Solutions Chapter 18 Surface Area and Volume of 3D Solids Chapter Test

Question 1.

The areas of three consecutive faces of a cuboid are 12 cm^{2}, 20 cm^{2} and 15 cm^{2}, then the volume (in cm^{2}) of the cuboid is

(a) 3600

(b) 100

(c) 80

(d) 60

Solution:

Area first face = (l × b) = 12 cm^{2}

Area of second face (b × l) = 20 cm^{2} and area of third face (h × l) = 15 cm^{2}

∴ l × b + b × h + h × l = 12 × 20 × 15

l^{2} b^{2} h^{2} = 3600 \\

lbh = \(\sqrt{3600}\) = 60

∴ Volume = 60 cm^{3}

Question 2.

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, the volume of the hall in cu m is

(a) 720

(b) 900

(c) 1200

(d) 1800

Solution:

Length of hall (l) = 15 m

and breadth (b) = 12 m

∴ Area of floor and ceiling = 2 × lb

= 2 × 15 × 12 = 360 m^{2}

∴ Area of walls = 360 m^{2}

⇒ 2 (l + b)h = 360 m^{2}

⇒ 2 (15 + 12)h = 360 ⇒ 2 × 27h = 360

⇒ h = \(\frac{360}{2 \times 27}\) = \(\frac{20}{3}\) m

∴ Volume = lbh = 15 × 12 × \(\frac { 20 }{ 3 }\) = 1200 m^{3}

Question 3.

Water flows into a tank which is 200 m long and 150 m wide through a pipe of cross section 0.3 × 0.2 m at 20 km/hr. Then the time (in hours) for the water level in the tank to reach 8 m is

(a) 50

(b) 120

(c) 150

(d) 200

Solution:

Length of tank (l) = 200 m

Width (b) = 150 m

Speed of water flow = 20 km/hr

Mouth of pipe = 0.3 × 0.2 m

= \(\frac { 3 }{ 10 }\) × \(\frac { 2 }{ 10 }\) = \(\frac { 6 }{ 100 }\)m^{2}

Water level in tank (h) = 8 m

Question 4.

A rectanguiar sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is

(a) 896 cm^{3}

(b) 986 cm^{3}

(c) 600 cm^{3}

(d) 916 cm^{3}

Solution:

Length of metal sheet = 40 cm

Breadth = 15 cm

Equal of each square cut out at each corner = 4 cm

∴ Remaining length = 40 – 2 × 4 = 40 – 8 = 32 cm

and width = 15 – 2 × 4 = 15 – 8 = 7 cm

∴ Length of so formed box = 32 cm

Width = 7 cm

and height = 4 cm

∴ Volume = lbh = 32 × 7 × 4 = 896 cm^{3}

Question 5.

Water is drawn out of a full tank. The shape of the tank is cuboid of length 3 m, breadth 1.4 m and depth 80 cm. If the rate of water flowing out is 100 cm^{3}/sec, then water level (in cms) in the tank after 5 minutes is

(a) 79\(\frac { 1 }{ 7 }\)

(b) 79\(\frac { 2 }{ 7 }\)

(c) 69\(\frac { 1 }{ 7 }\)

(d) 69\(\frac { 2 }{ 7 }\)

Solution:

Length of water tank (l) = 3 m = 300 cm

Width (b) = 1.4 m = 140 cm

Height (h) = 80 cm

∴ Volume of water = lbh

= 300 × 140 × 80 cm^{3} = 336000 cm^{3}

Speed of water flow = 100 cm/sec.

Water flow in 5 min. = 100 × 5 × 60 = 30000 cm^{3}

∴ Water level which flowed out = \(\frac{30000}{300 \times 140}\)

= \(\frac { 10 }{ 14 }\) = \(\frac { 5 }{ 7 }\)cm

∴ Water level remaining in the tank

= 80 – \(\frac { 5 }{ 7 }\) = 79\(\frac { 2 }{ 7 }\)cm

Question 6.

If S is the total surface area of a cube and V is its volume, then which one of the following is correct?

(a) V^{3} = 216 S^{2}

(b) S^{3} = 216 V^{2}

(c) S^{3} = 6 V^{2}

(d) S^{2} = 36V^{2}

Solution:

Let side of a cube = a

Then total surface area = 6 a^{2} = S

and volume = a^{3} = V

S^{3} = (6a^{2})^{3} = 216a^{6} = 216(V)^{2} = 216V^{2}

Question 7.

If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm^{2} respectively, then the maximum length of a stick that can be placed inside the box is

(a) 5 √2 cm

(b) 5 cm

(c) 6 cm

(d) 2√5 cm

Solution:

Sum of three dimension of a cuboid box = 12 cm and total surface area = 94 cm^{2}

= 2(lb + bh + hl) = 94 cm^{2}

Now largest stick (diagonal)

= \(\sqrt{l^2+b^2+h^2}\)

l + b + h = 12

Squaring both sides,

l^{2} + b^{2} + h^{2} + 2 (lb + bh + hl) = 144

⇒ l^{2} + b^{2} + h^{2} + 94 = 144

⇒ l^{2} + b^{2} + h^{2} = 144 – 94 = 50

\(\sqrt{l^2+b^2+h^2}\) = \(\sqrt{50}\)

= \(\sqrt{25 \times 2}\) = 5√2 cm

Question 8.

The diagonal of a cube is 4√3 cm. What is its volume?

(a) 16 cu cm

(b) 32 cu cm

(c) 64 cu cm

(d) 192 cu cm

Solution:

Diagonal of a cube = 4√3 cm

Let a be the side of cube

∴ Volume = a^{3}

and √3 a = diagonal

∴ a√3 = 4√3 ⇒ a = 4

and volume = (4)^{3} = 64 cm^{3}

Question 9.

If three cubic biscuits having edges 0.3 m, 0.4 m and 0.5 m respectively are melted and formed into a single cubic biscuits, then what is the total surface area of the cubic biscuit?

(a) 1.08 sq m

(b) 1.56 sq m

(c) 1.84 sq m

(d) 2.16 sq m

Solution:

Side of first cube biscuit = 0.3 m

Volume = (0.3)^{3} = 0.027 m^{3}

Side of second cube = 0.4 m

∴ Volume (0.4)^{3} = 0.064 m^{3}

and side of third cube = 0.5 m

∴ Volume = (0.5)^{3} = 0.125 m^{3}

Total volume of 3 cubes

=0.027 + 0.064 + 0.125 = 0.216 m^{3}

∴ Side of single cube so formed = \(\sqrt[3]{0.216} \mathrm{~m}\) = 0.6 m

and total surface area = 6(side)^{2}

= 6 × (0.6)^{3} = 6 × 0.36 m^{2}

= 2.16 m^{2}

Question 10.

In order to fix an electric pole along a roadside, a pit with dimensions 50 cm × 50 cm is dug with the help of a spade. The pit is prepared by removing earth by 250 strokes of spade. If one stroke of spade removes 500 cm^{3} of earth, then what is the depth of the pit?

(a) 2 m

(b) 1 m

(c) 0.75 m

(d) 0.5 m

Solution:

Length of pit = 50 cm

and breadth = 50 cm

Volume of one strok of spade removed from earth = 500 cm^{3}

Total volume of 250 strokes = 250 × 500 cm^{3}

= 125000 cm^{3}

∴Depth of pit = \(\frac{\text { Volume }}{l \times b}\)

= \(\frac{125000}{50 \times 50}\) = 50 cm = 0.5 m