Question

The curved surface area of a hemisphere is $$77c{m}^2$$. The radius of the hemisphere is:
(a)3.5cm
(b)7cm
(c)10.5cm
(d)11cm

Answer 1

Hint: As the value of curved surface area is given as $$77c{m}^2$$ use the formula $$2\pi r^2$$ and equate it with 77, where r represents radius.

Complete step-by-step answer:
In the question we are given the value of the curved surface area of the hemisphere which is $$77c{m}^2$$ and we have to find the radius of the hemisphere from the given data.
Before proceeding we will learn briefly about hemispheres.
A hemisphere is the half part of a sphere. We can find many of the real life examples of the hemispheres such as our planet earth can be divided into two segments the northern and southern hemispheres we primarily find out the curved surfaces area and the total surface area. The area of the outer portion is constituted on the curved surface area is obtained by addition of curved surface area and base area of hemisphere.
The surface area is the area occupied by the surface of the solid object. The surface area is classified into two types namely:
Curved Surface Area (C.S.A)
Total Surface Area (T.S.A)
The Curved Surface area of hemisphere is denoted by formula $$2\pi r^2$$, where r is radius of hemisphere and $$\pi$$ is $${\displaystyle \frac{22}{7}}$$.
So, we can write that,
$$2\pi r^2=77$$
Or, $$2\times {\displaystyle \frac{22}{7}}\times r^2=77$$
So, $$r^2={\displaystyle \frac{77\times 7}{2\times 22}}$$
Or, $$r^2={\displaystyle \frac{49}{4}}$$
Hence, $$r={\displaystyle \frac{7}{2}}$$ or 3.5cm
So, the correct option is (a).

Note: Generally students confuse between curved surface and total surface area. Curved surface area only includes the curved part while total surface area also includes the area of base.