Question

John's birthday cake is a delightful cylinder of radius 6 inches and height 3 inches. If these friends cut the cake into 8 equal sectors, then the total surface area of a piece of birthday cake in sq. inches is

• A. $9(\pi +4)$
• B. $\frac{27\pi }{2}$
• C. $4(\pi +4)$
• D. $\frac{9}{2}(3\pi +8)$

Answer 1

The correct option is D $\frac{9}{2}(3\pi +8)$

Area of the rectangles on either side of the wedge = $2\times radius\times height=2\times 18=36sqcm.$
Area of the sector (top and bottom) = $2\times \frac{45}{360}\times \pi \times 6^2=9\pi sqcm$
Curved area of the cylinder = $\frac{2\pi \times 6\times 3}{8}=\frac{9}{2}\pi sqcm$.
Total area of each wedge = $\frac{9}{2}\pi +9\pi +36=36+\frac{27}{2}\pi =\frac{9}{2}(3\pi +8)sqcm$