Question

A skating board rocks back and forth on a wooden cylinder. The cylinder has a radius of 6 inches and a surface area is $590{in}^2$. Find the height of the cylinder. ($\pi =3.14$).

• A. $10$ in
• B. $9.65$ in
• C. $9$ in
• D. $9.5$ in

Answer 1

The correct option is B $9.65$ in

Surface area of cylinder is $A=2\pi r(r+h)$

Here the wooden cylinder has surface area $A=590$ in${}^2$ and radius $r=6$ mm.

Thus,

$A=2\pi r(r+h)\Rightarrow 590=2\times \frac{22}{7}\times 6(6+h)\Rightarrow 590=\frac{44}{7}(36+6h)\Rightarrow 590\times 7=1584+264h\Rightarrow 4130-1584=264h\Rightarrow 264h=2546\Rightarrow h=\frac{2546}{264}=9.643$

Hence, the height of the wooden cylinder is $9.65$ in.