Question : 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 cm$^2$. What is the volume (in cm$^3$) of the prism?
Option 1: 540
Option 2: 600
Option 3: 720
Option 4: 640
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Correct Answer: 720
Solution :
Given: Lateral surface area of prism = 480 cm
2
Lateral surface area of prism = perimeter of base × height
Perimeter of triangle = 8 + 15 + 17 = 40 cm
Let the height of the prime is $h$ cm
⇒ $40 × h = 480$
⇒ $h = 12$ cm
Since the base, the side and the length are 8, 15, and 17 which are triplets.
It means the base is a right-angled triangle
Area of triangular base = $\frac{1}{2} × 8 × 15$ = 60 cm
2
So, the volume of the prism = area of base × height
= 60 × 12 = 720 cm
3
Hence, the correct answer is 720.
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