Surface Area of a Sphere Formula
A sphere can be called a three-dimensional equivalent of a circle. It is a collection of points in tri space that are all at the same distance from a particular point. This distance is regarded as the radius of the said sphere.
Surface Area of Sphere
The total area of a sphere refers to the region covered by the sphere’s outer surface. The three-dimensional version of a circle is known as a sphere. A sphere differs from a circle in the aspect that a circle is a two-dimensional (2D) form, but a sphere is a three-dimensional (3D) shape. A sphere’s surface area is measured in square units.
Formula
A = 4πr2
where r denotes the radius of the given sphere.
Sample Problems
Problem 1. Find the surface area of a sphere whose radius is 5 m.
Solution:
Given: r = 5 m
Since, A = 4πr2
= 4 × 3.14 × 52
= 4 × 3.14 × 25
A = 314 m2
Problem 2. Find the surface area of a sphere of radius 10 m.
Solution:
Given: r = 10 m
Since, A = 4πr2
= 4 × 3.14 × 102
= 4 × 3.14 × 100
A = 1256 m2
Problem 3. What would be the cost of painting a sphere of radius 4.5 cm at INR 5 per sq. cm?
Solution:
Given: r = 4.5 cm
TSA = 4πr2
= 4 × 3.14 × 4.52
= 254.47 cm2
So, total cost of painting the sphere = 254.47 × 5
= INR 1272.35
Problem 4. What would be the cost of painting a sphere of radius 3 cm at INR 12 per sq. cm?
Solution:
Given: r = 4.5 cm
TSA = 4πr2
= 4 × 3.14 × 32
= 113.04 cm2
So, total cost of painting the sphere = 113.04 × 12
= INR 1356.48
Problem 5. Find the surface area of a sphere of radius 15 m.
Solution:
Given: r = 15 m
Since, A = 4πr2
= 4 × 3.14 × 152
= 4 × 3.14 × 225
A = 2826 m2
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