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The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is
(a) 192
(b) 384
(c) 480
(d) 2592

Solution:

If we assume the Length, breadth and height of the rectangular solid to l, b and h respectively we have::

b × h = 16 (1)

l × h = 32 (2)

l × b = 72 (3)

Dividing (2) by (1) we get,

l/b = 2

l = 2b

Substituting l = 2b in equation (3) we get

2b × b = 72

2b² = 72

b² = 36

b = 6

Substituting the value of b in (3) we have

l × 6 = 72

l=12

Substituting the value of l in (2) we get

12 × h = 32

h = 8/3

Volume = l × b × h = 12 × 6 × (8/3) = 192 cm³

✦ Try This: The surface areas of the six faces of a rectangular solid are 8, 8, 16, 16, 32 and 32 square centimetres. The volume of the solid, in cubic centimetres, is (a) 128, (b) 64, (c) 96, (d) 216

If we assume the Length, breadth and height of the rectangular solid to l, b and h respectively we have::

b × h = 8 (1)

l × h = 16 (2)

l × b = 32 (3)

Dividing (2) by (1) we get,

l/b = 2

l = 2b

Substituting l = 2b in equation (3) we get

2b × b = 32

2b² = 32

b² = 16

b = 4

Substituting the value of b in (3) we have

l × 4 = 32

l=8

Substituting the value of l in (2) we get

8 × h = 16

h = 2

Volume = l × b × h = 8 × 4 × 2 = 64 cm³

The correct answer is choice (b).

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 26

The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is (a) 192 (b) 384 (c) 480 (d) 2592

Summary:

The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is 192 cm³

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