Question

There is a solid cylinder of base radius 5 cm and height 10 cm. From one of the flat ends of the solid cylinder a hemispherical depression having same radius as cylinder is hollowed out. What is the total surface area (in sq.cm) of this new solid?

• A. 175$\pi$
• B. 75$\pi$
• C. 100$\pi$
• D. 120$\pi$

Answer 1

The correct option is A

175$\pi$

The total surface area of the above solid = C.S.A of the hemispherical depression + C.S.A of the cylinder + Base area of the cylinder

C.S.A of hemispherical depression $=2\pi r^2=2\pi (5{)}^2=50\pi c{m}^2$

C.S.A of cylinder $=2\pi rh=2\pi \times 5\times 10=100\pi c{m}^2$

Base area of cylinder = $\pi$$r^2$

= $\pi$$(5{)}^2$

= 25$\pi$ $c{m}^2$

Total surface area = C.S.A of hemispherical depression + C.S.A of cylinder + Base area of cylinder$=50\pi +100\pi +25\pi =175\pi$