The surface area of the three coterminus faces of a cuboid are 6cm², 15 cm² and 10 cm² respectively. The volume of the cuboid is
(a) 30 cm³
(b) 40 cm³
(c) 20 cm³
(d) 35 cm³
Solution:
The information in the problem is summarized in the diagram below:
Therefore,
l × h = 15 cm² (1)
b × h = 6 cm² (2)
l × b = 10 cm² (3)
Dividing (1) by (2) we have
l/b = 15/6 = 5/2
l = 5b/2 (4)
From (3) we have
l × b = 10 cm²
Substituting (4) in above we get
(5b/2) × b = 10
b² = (10 × 2)/5 = 4
b = 2
Therefore from (3)
l = 5
From (1)
h = 3
Therefore we have the three required dimensions:
l = 5; b = 2; h = 3
Therefore the volume of V of the cuboid is,
V = l × b × h = 5 × 2 × 3 = 30cm³
The answer is choice (a)
✦ Try This: The surface area of the three coterminus faces of a cuboid are 9cm², 22.5 cm² and 15cm² respectively. The volume of the cuboid is
(a) 30 cm³ (b) 40 cm³ (c) 20 cm³ (d) 35 cm³
The cuboid described in the problem is given below:
Therefore,
l × h = 22.5 cm² (1)
b × h = 9 cm² (2)
l × b = 15 cm² (3)
Dividing (1) by (2) we have
l/b = 22.5/9 = 5/2
l = 5b/2 (4)
From (3) we have
l × b = 10 cm²
Substituting (4) in above we get
(5b/2) × b = 15
b² = (10 × 2)/5 = 6
b = √6
Therefore from (3)
l = 15/√6
From (1)
h = (22.5)/(15/√6)
h = 1.5 × √6
Therefore we have the three required dimensions:
l = 15/√6, b = √6; h = 1.5√6
Therefore the volume of V of the cuboid is,
V = l × b × h = (15/√6)×√6 ×1.5√6 = 22.5√6 cm³
The answer is choice
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 8
The surface area of the three coterminus faces of a cuboid are 6cm², 15 cm² and 10 cm² respectively. The volume of the cuboid is (a) 30 cm³ (b) 40 cm³ (c) 20 cm³ (d) 35 cm³
Summary:
The surface area of the three coterminus faces of a cuboid are 6cm², 15 cm² and 10 cm² respectively. The volume of the cuboid is 30cm³
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