The base of a right prism is a triangle whose sides are 8 cm, 15 cm and 17 cm, and its lateral surface area is 480 cm². What is the volume (in cm³) of the prism?

Question

Question

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 2 (Held On: 3 Feb 2022)

Answer 1

Given:

The base of a right prism is a triangle whose sides are 8 cm, 15 cm and 17 cm

The lateral surface area of right prism 480 cm2

Formula Used:

Lateral surface area of prism = perimeter of base × height

Volume of prism = Area of base × height

Calculation:

F2 Savita SSC 5-5-22 D13

Since base side length is 8, 15, 17 [which is a triplet]

It means the base is a right angled triangle

Perimeter of triangle = 8 + 15 + 17 = 40 cm

Let the height of the prime is h cm

So, 40 × h = 480

⇒ h = 12 cm

Now, Area of base = (1/2) × 8 × 15 = 60 cm²

Volume of prism = area × height

∴ Volume of prism = 60 × 12 = 720 cm³.

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