Question

Find the total surface area of a hollow right circular cylinder with an inner radius equal to r, outer radius equal to R and height is h.

• A. 2 $\pi (R+r)(h+\frac{R}{2}+\frac{r}{2}$)
• B. 2 $\pi (R+r)(h+R-r$)
• C. 2 $\pi (R+r)(h+\frac{R}{2}-\frac{r}{2}$)
• D. $2\pi (R+r)(h-R+r)$

Answer 1

The correct option is B

2 $\pi (R+r)(h+R-r$)

We know that,
Curved surface area of cylinder
$=2\pi rh$
Area of circular base
$=\pi r^2$

Now, total surface area of cylinder
=2$\pi$rh + 2$\pi$Rh + $2\pi R^2$ - $2\pi r^2$
= 2$\pi$ (R + r)h + $2\pi$ ($R^2$-$r^2$)
= 2 $\pi$ (R + r)h + $2\pi$ (R + r)(R - r)
= 2 $\pi$ (R + r)( h + $R-r$)