Question 63

Base of a right prism is an equilateral triangle of side 6 cm. If the volume of the prism is 108 $$\sqrt{3}$$cc. its height is

Solution

area of the base = $$ \frac{\sqrt 3}{4} \times side^2 $$

= $$ \frac{\sqrt 3}{4} \times 6 \times 6 $$

= $$ 9\sqrt3 cm^2 $$

therefore, volume of the prism = $$ area of base \times height $$

$$ 108\sqrt 3 = 9\sqrt 3 \times h $$

solving h = $$ \frac{108 \sqrt 3}{9 \sqrt 3} = 12 $$

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