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Mathematics

A cuboid has length = 4 cm, breadth = 3 cm and diagonal = 13 cm. The volume of the cuboid is :

  1. 156 cm3

  2. 288 cm3

  3. 144 cm3

  4. 78 cm3

Mensuration

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Answer

Given:

Length of cuboid = 4 cm

Breadth of cuboid = 3 cm

Diagonal of cuboid = 13 cm

Let h be the height of cuboid.

Length of diagonal of cuboid = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

⇒ 42+32+h2\sqrt{4^2 + 3^2 + h^2} = 13

⇒ 16+9+h2\sqrt{16 + 9 + h^2} = 13

Squaring both sides, we get

⇒ (16+9+h2)2({\sqrt{16 + 9 + h^2}})^2 = (13)2

⇒ 16 + 9 + h2 = 169

⇒ 25 + h2 = 169

⇒ h2 = 169 - 25

⇒ h2 = 144

⇒ h = 144\sqrt{144}

⇒ h = 12 cm

Volume of cuboid = l x b x h

= 4 x 3 x 12 cm2

= 144 cm2

Volume of cuboid is 144 cm2.

Hence, option 3 is the correct option.

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