Question : The base of a right prism is a triangle with sides 16 cm, 30 cm, and 34 cm. Its height is 32 cm. The lateral surface area (in cm2 ) and the volume (in cm3 ) are, respectively:
Option 1: 2560 and 7680
Option 2: 2688 and 7680
Option 3: 2624 and 7040
Option 4: 2560 and 6400
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Correct Answer: 2560 and 7680
Solution :
Here, (34)
2
= (16)
2
+ (30)
2
⇒ 1156 = 256 + 900
So, 16, 30, and 34 are the sides of a right-angled triangle.
⇒ Volume of Prism = Area of base × height
= $\frac{1}{2}$ × 16 × 30 × 32 cm
3
= (8 × 30 × 32) cm
3
= 7680 cm
3
Now, lateral surface area of the prism = perimeter of base × height = (16 + 30 + 34) × 32 cm
2
= 2560 cm
2
Hence, the correct answer is 2560 and 7680.
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