Question

The surface area of the three
coterminous faces of cuboid are 6 cm?
15 cm2 and 10 cmrespectively. Then,
what will be the volume of the cuboid?
(A) 30 cm3
(B) 40 cm
(C)20 cm3
(D) 35 cm3​

Answer 1

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Given : The surface area of the three coterminous faces of a cuboid are 6 cm² ,15 cm² , and 10 cm² respectively.

To find : What is the volume of the cuboid?

Solution :

Let l,b,h be the dimensions of the cuboid.

The surface area of the three coterminous faces of a cuboid are 6 cm² , 15 cm² , and 10 cm² respectively.

i.e. $l\times b=6$...(1)

$b\times h=15$ ...(2)

$h\times l=10$ ...(3)

Volume of the cuboid is V=lbh

Multiply (1),(2) and (3),

$l\times b\times b\times h\times h\times l=6\times 15\times 10$

⇒$l^2\times b^2\times h^2=900$

⇒ $(lbh)^2=900$

⇒$lbh=\sqrt{900}$

⇒$lbh=30$

Therefore, the volume of the cuboid is 30 cm³.

Answer 2

$\dag\:\underline{\sf Question:-}$

The surface area of the three  coterminous faces of cuboid are 6 cm², 15 cm² and 10 cm² respectively. Then,  what will be the volume of the cuboid?

(a) 30 cm³

(b) 40 cm³

(c)20 cm³

(d) 35 cm³

$\dag\:\underline{\sf Answer:-}$

Given:-

• Surface area of three coterminous faces of a cuboid are 6 cm², 15 cm² and 10 cm².

To find:-

• Volume of the cuboid

Solution:-

Let 'l','b' and 'h' be the dimensions of the cuboid.

The surface area of three coterminous faces of a cuboid are 6 cm², 15 cm² and 10 cm², that is,

l × b = 6 cm² -----eqⁿ.1

b × h = 15 cm² -----eqⁿ.2

h × l = 10 cm² -----eqⁿ.3

We know that,

     Volume of a cuboid = lbh

Multiplying eqⁿ.1, 2 and 3,

(l × b) (b × h) (h × l) = (6) (10) (15)

(l²) (b²) (h²) = 900

(lbh)² = 900

lbh = √900

lbh = 30

Volume = lbh = 30

∴ Volume of the cuboid = 30cm³

∴ Option (a) 30 cm³ is the correct one.

★LEARN MORE:-

Find the volume of cuboid(with steps)

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