Question 144

Height of a prism-shaped part of a machine is 8 cm and its base is an isosceles triangle, whose each of the equal sides is 5 cm and remaining side is 6 cm. The volume of the part is

Solution

Given height of the prism = 8 cm .........(1)

Area of the base,

$$\Rightarrow \frac{b}{4} \sqrt{4a^{2} - b^{2}}$$ (here a = 5, b = 6)

$$\frac{6}{4} \sqrt{4(5)^{2} - 6^{2}}$$

$$ \frac{3}{2}\sqrt{64} = 12$$ .......(2)

Volume of the part = Area of the base x height of the prism

Substitute equation (1) and (2) in the above equation

Volume of the part = 12 x 8 = 96 cm

Hence, option D is the correct answer.

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