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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?

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? Correct Answer 720

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:

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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