# 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

**☛ Related Questions:**

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