Question : The base of a prism is a right-angle triangle whose sides are 9 cm, 12 cm, and 15 cm. Volume of this prism is 648 cm3. What will be the height of the prism?
Option 1: 14 cm
Option 2: 12 cm
Option 3: 9 cm
Option 4: 16 cm
Correct Answer: 12 cm
Solution :
Given: The base of a prism is a right-angle triangle whose sides are 9 cm, 12 cm, and 15 cm.
The volume of this prism is 648 cm
3
.
Base area = $\frac{1}{2}$ × Perpendicular × Base
= $\frac{1}{2}$ × 9 × 12 = 54 cm
2
The volume of the prism = Base area × Height
⇒ 648 = 54 × Height
⇒ Height = 12 cm
So, the height of the prism = 12 cm
Hence, the correct answer is 12 cm.
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