Question

A circular cylinder with a volume of $6.54cu.m$ is circumscribed about a right prism whose base is an equilateral triangle of side $1.25m$. What is the altitude of the cylinder in meters?

• A. $3.5$
• B. $3.75$
• C. $4.0$
• D. $4.25$

Answer 1

The correct option is C $4.0$

Given : Volume of prism $=6.54cu.m.$ Side of equilateral triangle$\left(l\right)=1.25m$

Height of equilateral triangle$\left(h\right)=\frac{\sqrt{3}}{2}\left(l\right)$

$=\frac{\sqrt{3}}{2}\times 1.25$

The center of the circle is the centroid and height coincides with the median.

$\therefore$ Radius of circumcircle$\left(r\right)=\frac{2}{3}h$

$=\frac{2}{3}\times \frac{\sqrt{3}}{2}\left(1.25\right)$

$=\frac{1.25}{\sqrt{3}}$

Area of circumcircle $=\pi r^2$

Volume of cylinder$\left(V\right)=Areaofbase\times altitude$

$\therefore$ Altitude $=\frac{Volume}{Area}$

$=\frac{6.54}{\pi (\frac{1.25}{\sqrt{3}}{)}^2}$

$=\frac{6.54\times 3}{1.5625\pi }$

$=4.0$

Hence, altitude of a cylinder is $4.0$.