Question

When the figure above is spun around its vertical axis, the total surface area of the solid formed will be

• A. $144\pi$
• B. $108\pi$
• C. $72\pi$
• D. $36\pi$
• E. $9\pi +12$

Answer 1

The correct option is B $108\pi$

The figure formed when the figure is rotated about the vertical axis is a hemisphere, therefore, the total surface area of the figure is the area of the hemisphere that is $2\pi r^2$ plus the area of circle that is $\pi r^2$.

It is given that the radius $r=6$, the area of the solid is as follows:

$A=2\pi r^2+\pi r^2$

$=2\pi (6{)}^2+\pi (6{)}^2$

$=72\pi +36\pi$

$=108\pi$