RS Aggarwal Class 8 Solutions Chapter 20 Volume and Surface Area of Solids Ex 20C
These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 20 Volume and Surface Area of Solids Ex 20C.
Other Exercises
- RS Aggarwal Solutions Class 8 Chapter 20 Volume and Surface Area of Solids Ex 20A
- RS Aggarwal Solutions Class 8 Chapter 20 Volume and Surface Area of Solids Ex 20B
- RS Aggarwal Solutions Class 8 Chapter 20 Volume and Surface Area of Solids Ex 20C
Tick the correct answer in each of the following:
Question 1.
 Solution:
 Answer = (b)
 Length (l) = 12 cm
 Breadth (b) = 9cm
 height (h) = 8 cm
 
Question 2.
 Solution:
 Total surface area of cube = 150 cm2
 Side = \( \sqrt { \frac { 150 }{ 6 } } \)
 = √25
 = 5 cm
 Volume = (side)3
 = (5)3
 = 125 cm3 (b)
Question 3.
 Solution:
 Volume of cube = 343 cm2
 Side = \( \sqrt [ 3 ]{ 343 } =\sqrt [ 3 ]{ 7\times 7\times 7 } \)
 = 7 cm
 Total surface area = 6 (side)2
 = 6 x (7)2
 = 6 x 49 cm2
 = 294 cm2 (c)
Question 4.
 Solution:
 Rate of painting = 10 paise per cm2
 Total cost = Rs. 264.60
 
Question 5.
 Solution:
 Answer = (c)
 Length of wall (l) = 8m = 800 cm
 Breadth (b) = 22.5 cm
 Height (h) = 6 m
 = 600 cm
 
Question 6.
 Solution:
 Answer = (c)
 Edge of cube = 10 cm
 Volume = a3 = (10)3 = 1000 cm3
 Edge of box = 1 m = 100 cm
 
Question 7.
 Solution:
 Answer = (a)
 Ratio in sides of a cuboid = 1 : 2 : 3
 Surface area = 88 cm2
 
Question 8.
 Solution:
 Ratio in the two volumes = 1 : 27
 Let volume of first volume = x3
 and volume of second volume = 27x3
 Side of first cube = x
 
Question 9.
 Solution:
 Surface area of a brick of measure 10 cm x 4 cm x 3 cm
 = 2 (l x b + b x h + h x l)
 = 2 [10 x 4 + 4 x 3 + 3 x 10] cm2
 = 2 [40 + 12 + 30]
 = 82 x 2
 = 164 cm2 (c)
Question 10.
 Solution:
 Length of beam (l) = 9 m
 
Question 11.
 Solution:
 Water in rectangular reservoir = 42000
 Volume = \(\\ \frac { 42000 }{ 1000 } \) = 42 m3
 Length (l) = 6 m
 Breadth (b) = 3.5 m
 Depth = \(\\ \frac { volume }{ l\times b } \)
 = \(\\ \frac { 42 }{ 6\times 3.5 } \)
 = 2 m (c)
Question 12.
 Solution:
 Dimensions of a room are 10 m, 8 m, 3.3 m
 Volume of air in it = lbh
 = 10 x 8 x 3.3 = 264 m3
 Air required for one man = 3 m3
 No. of men = \(\\ \frac { 264 }{ 3 } \)
 = 88 (b)
Question 13.
 Solution:
 Length of water tank (l) = 3 m
 Width (b) = 2 m
 and height (h) = 5 m
 Volume = lbh = 3 x 2 x 5 = 30 m3
 Water in it = 30 x 1000
 = 30000 (a)
Question 14.
 Solution:
 Size of box = 25 cm, 15 cm, 8 cm
 Surface area = (lb + bh + hl)
 = 2 ( 25 x 15 + 15 x 8 + 8 x 25) cm2
 = 2 (375 + 120 + 200) cm2
 = 2(695)
 = 1390 cm2 (b)
Question 15.
 Solution:
 Diagonal of cube = 4√3
 Side = \( \frac { 4\sqrt { 3 } }{ \sqrt { 3 } } \)
 = 4 cm
 Volume = a3 = (4)3
 = 64 cm3 (d)
Question 16.
 Solution:
 Diagonal of cube = 9√3 cm
 Side = \( \frac { 9\sqrt { 3 } }{ \sqrt { 3 } } \)
 = 9 cm
 Surface area = 6a2
 = 6 (9)2 = 6 x 81 cm2
 = 486 cm2 (b)
Question 17.
 Solution:
 Let side of cube in first case = a
 Then volume = a3
 If side of cube is doubled, then side = 2a
 Volume (2a)3 = 8a3
 Becomes 8 times (d)
Question 18.
 Solution:
 Let side of cube in first case = a
 Then surface area = 6a2
 and side of second cube = 2a
 Surface area = 6 (2a)2 = 6 x 4a2 = 24a2
 Ratio = \(\frac { { 24a }^{ 2 } }{ { 6a }^{ 2 } } \) = 4
 Becomes 4 times (b)
Question 19.
 Solution:
 Sides (edges) of 3 cubes are 6 cm, 8 cm, and 10 cm respectively
 Volume of first cube = (6)3 = 216 cm3
 Volume of second cube = (8)3 = 512 cm3
 and volume of third cube
 = (10)3 = 1000 cm3
 Sum of volumes of 3 cubes = 216 + 512 + 1000
 = 1728 cm3
 Volume of new single cube = 1728 cm3
 Edge = \(\sqrt [ 3 ]{ 1728 } \)
 \(\sqrt [ 3 ]{ { \left( 12 \right) }^{ 3 } } \)
 = 12 cm (a)
Question 20.
 Solution:
 Each edge of 5 cubes = 5 cm
 Placing than adjacent to each other
 Length of new cuboid (l)
 = 5 x 5 = 25 cm
 Breadth (b) = 5 cm
 and height (h) = 5 cm
 Volume of new cuboid = lbh
 = 25 x 5 x 5 cm3
 = 625 cm3 (d)
Question 21.
 Solution:
 Diameter of circular well = 2n
 Radius = \(\\ \frac { 2 }{ 2 } \) = 1 m
 Depth(h) = 14 m
 Volume of earth dug out = πr2h
 = \(\\ \frac { 22 }{ 7 } \) x 1 x 1 x 14
 = 44 m (d)
Question 22.
 Solution:
 Capacity of cylindrical tank = 1848 m3
 Diameter = 14 m
 
Question 23.
 Solution:
 Radius of a cylinder (r) = 20 cm
 and height (h) = 60 cm
 
Question 24.
 Solution:
 Radius of each coin (r) = 0.75 cm
 and thickness (h) = 0.2 cm
 
Question 25.
 Solution:
 Volume of silver = 66 cm3
 Diameter of wire = 1 mm = \(\\ \frac { 1 }{ 10 } \)
 
Question 26.
 Solution:
 Diameter of cylinder = 10 cm
 Radius (r) = \(\\ \frac { 10 }{ 2 } \) = 5 cm
 
Question 27.
 Solution:
 Diameter of cylinder = 7 cm
 Radius (r) = \(\\ \frac { 7 }{ 2 } \) cm
 
Question 28.
 Solution:
 Curved surface area of a cylinder = 264 cm3
 Height (h) = 14 cm
 
Question 29.
 Solution:
 Diameter of cylinder = 14 cm
 Radius (r) = 7 cm
 Curved surface area = 220 cm2
 
Question 30.
 Solution:
 Ratio in radii of two cylinder = 2 : 3
 and ratio in their height = 5 : 3
 Let radii of two cylinder = 2x and 3x
 and corresponding heights = 5y, 3y
 
Hope given RS Aggarwal Solutions Class 8 Chapter 20 Volume and Surface Area of Solids Ex 20C are helpful to complete your math homework.
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