Question

The perimeter of a triangular base of a right prism is 15 cm and radius of the in circle of the triangular base is 3 cm.If the volume of the prism be 270 cubic.Then what will be its height ?

Answer 1

The perimeter of a triangular base of a right prism is $15\mathrm{cm}$ and radius of the in circle of the triangular base is $3\mathrm{cm}$ . If the volume of the prism be 270 (cubic cm) then what will be its height?

Solution:

We have

$$S = \frac {1}{2} r a + \frac {1}{2} r b + \frac {1}{2} r c = \frac {1}{2} r (a + b + c) = \frac {1}{2} \cdot 3 \cdot 1 5 = 2 2, 5 (c m ^ {2})$$

where $S$ is the square of the triangular base of the right prism. If $h$ is the height of the right prism then the volume of one is

$$V = S h = 2 7 0,$$ $$2 2, 5 h = 2 7 0,$$ $$h = 1 2 (c m).$$

Answer: $h = 12(cm)$