Question

Find the surface area of a sphere of radius.
  (i) 10.5cm (ii)5.6cm (iii)14cm

Answer 1

Hint: Use surface area of the sphere formula to solve the problem separately for each case.
Formula used: Surface area of a sphere is $4\pi {r^2}$ where ‘r’ is the radius of the sphere and $\['\pi '\]$ is equal to 22/7 or 3.14.

Complete step-by-step solution:
(i)10.5cm
In this case, we are given that the radius of the sphere is 10.5cm.
r=10.5cm.
Surface area of the sphere $ = 4\pi {r^2}$
$
   = 4 \times \pi \times r \times r \\
   = 4 \times \dfrac{{22}}{7} \times 10.5 \times 10.5 \\
   = 4 \times \dfrac{{22}}{{{{{7}}_2}}} \times {1}{0}.{{{5}}^3} \times 10.5 \\
   = 4 \times \dfrac{{2{{{2}}^{11}}}}{{{{{2}}_1}}} \times 3 \times 10.5 \\
   = 4 \times 11 \times 3 \times 10.5 \\
   = 1386c{m^2} \\
 $
Therefore, the surface of the sphere with radius 10.5cm is 1386 square centimeter.
(ii)5.6cm
In this case, we are given that the radius of the sphere is 5.6cm.
r=5.6cm.
Surface area of the sphere $ = 4\pi {r^2}$
$
   = 4 \times \pi \times r \times r \\
   = 4 \times \dfrac{{22}}{7} \times 5.6 \times 5.6 \\
   = 4 \times \dfrac{{22}}{{{{{7}}_1}}} \times {5}.{{{6}}^{0.8}} \times 5.6 \\
   = 4 \times 22 \times 0.8 \times 5.6 \\
   = 394.24c{m^2} \\
 $
Therefore, the surface of the sphere with radius 5.6cm is 394.24 square centimeter.
(iii)14cm
In this case, we are given that the radius of the sphere is 14cm.
r=14cm
Surface area of the sphere $ = 4\pi {r^2}$
$
   = 4 \times \pi \times r \times r \\
   = 4 \times \dfrac{{22}}{7} \times 14 \times 14 \\
   = 4 \times \dfrac{{22}}{{{{{7}}_1}}} \times 1{{{4}}^2} \times 14 \\
   = 4 \times 22 \times 2 \times 14 \\
   = 2464c{m^2} \\
 $
Therefore, the surface of the sphere with radius 14cm is 2464 square centimeter.

Note:The formula for the lateral surface area of a sphere is the same as the formula for the surface area of a sphere, since it has no bases. Thus, the lateral surface area of a sphere is $4\pi {r^2}$ , where r = radius of the sphere. Whereas the figures like cylinders, cones, cuboids, cubes have both lateral or curved surface area and total surface area.