Question

In Figure $2$, the bases of the right uniform solid are triangles with sides of lengths $5,12$ and $13$. If the surface area of the solid is $360$, calculate the volume.

• A. $30$
• B. $180$
• C. $300$
• D. $600$
• E. $780$

Answer 1

Answer: (C)

$300$

Surface area of solid is $2\times \frac{1}{2}\times 12\times 5+12\times b+5\times b+13\times b=60+30b=360$
$\Rightarrow b=10$
Let $h$ be height of triangle, we have $\frac{1}{2}\times h\times 13=\frac{1}{2}\times 5\times 12$

$\Rightarrow h=\frac{60}{13}$
Volume of solid is $\frac{1}{2}\times \frac{60}{13}\times 13\times 10=300$