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JIPMAT 2026 PYQsQuantitative Ability. Free, no login required.

Geometry

past year questions, JIPMAT 2026

Solids

past year questions, Geometry, JIPMAT 2026

Medium

The sum of length, breadth and height of a cuboid is 22 cm and the length of its body diagonal is 14 cm. What is the surface area of the cuboid?

Solution

✅ Correct Option: 1

Let the sides be ll, bb and hh.

l+b+h=22l+b+h=22

Using the formula for the body diagonal of a cuboid, l2+b2+h2\sqrt{l^2+b^2+h^2}:

l2+b2+h2=14\sqrt{l^2+b^2+h^2}=14

⇒l2+b2+h2=196\Rightarrow l^2+b^2+h^2=196

Using the identity (l+b+h)2=l2+b2+h2+2(lb+bh+hl)(l+b+h)^2=l^2+b^2+h^2+2(lb+bh+hl):

222=196+2(lb+bh+hl)22^2=196+2(lb+bh+hl)

⇒484−196=2(lb+bh+hl)\Rightarrow 484-196=2(lb+bh+hl)

⇒2(lb+bh+hl)=288\Rightarrow 2(lb+bh+hl)=288

The surface area of a cuboid is exactly 2(lb+bh+hl)2(lb+bh+hl), so the answer is already in front of us and we never need ll, bb and hh separately.

Surface area=288 cm2\text{Surface area}=288\text{ cm}^2

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