Question

The height and diameter of a right cylinder are equal the cylinder is surmounted by a hemispherical lid of radius $3$ inch then find the total area of the surface(approx.) of the modal is

• A. $154i{n}^2$
• B. $70i{n}^2$
• C. $54i{n}^2$
• D. $284i{n}^2$

Answer 1

Answer: (B)

$70i{n}^2$

Since the lid is of radius $3inch$, diameter of the cylinder $=6inch$.
=> height of the cylinder $=6inch$.

Surface area of the modal $=$
Curved surface area of hemispherical part $+$ Curved surface area if the
cylinderical part.
Curved surface area of a cylinder $=2\pi rh$ where r is the radius and h is the height.

Curved Surface Area of a hemisphere of radius 'r' $=2\pi r^2$

Hence, surface area of the modal $=(2\pi \times 3^2)+(2\pi \times 3\times 6)=54\pi m^2=69.7$ sq inch.