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 cm2, 20 cm2 and 15 cm2, then the volume (in cm2) of the cuboid is
(a) 3600
(b) 100
(c) 80
(d) 60
Solution:
Area first face = (l × b) = 12 cm2
Area of second face (b × l) = 20 cm2 and area of third face (h × l) = 15 cm2
∴ l × b + b × h + h × l = 12 × 20 × 15
l2 b2 h2 = 3600 \\
lbh = \(\sqrt{3600}\) = 60
∴ Volume = 60 cm3
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 m2
∴ Area of walls = 360 m2
⇒ 2 (l + b)h = 360 m2
⇒ 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 m3
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
= \(\frac { 3 }{ 10 }\) × \(\frac { 2 }{ 10 }\) = \(\frac { 6 }{ 100 }\)m2
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 cm3
(b) 986 cm3
(c) 600 cm3
(d) 916 cm3
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 cm3
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 cm3/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 cm3 = 336000 cm3
Speed of water flow = 100 cm/sec.
Water flow in 5 min. = 100 × 5 × 60 = 30000 cm3
∴ 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) V3 = 216 S2
(b) S3 = 216 V2
(c) S3 = 6 V2
(d) S2 = 36V2
Solution:
Let side of a cube = a
Then total surface area = 6 a2 = S
and volume = a3 = V
S3 = (6a2)3 = 216a6 = 216(V)2 = 216V2
Question 7.
If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm2 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 cm2
= 2(lb + bh + hl) = 94 cm2
Now largest stick (diagonal)
= \(\sqrt{l^2+b^2+h^2}\)
l + b + h = 12
Squaring both sides,
l2 + b2 + h2 + 2 (lb + bh + hl) = 144
⇒ l2 + b2 + h2 + 94 = 144
⇒ l2 + b2 + h2 = 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 = a3
and √3 a = diagonal
∴ a√3 = 4√3 ⇒ a = 4
and volume = (4)3 = 64 cm3
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 m3
Side of second cube = 0.4 m
∴ Volume (0.4)3 = 0.064 m3
and side of third cube = 0.5 m
∴ Volume = (0.5)3 = 0.125 m3
Total volume of 3 cubes
=0.027 + 0.064 + 0.125 = 0.216 m3
∴ 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 m2
= 2.16 m2
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 cm3 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 cm3
Total volume of 250 strokes = 250 × 500 cm3
= 125000 cm3
∴Depth of pit = \(\frac{\text { Volume }}{l \times b}\)
= \(\frac{125000}{50 \times 50}\) = 50 cm = 0.5 m