In this note, you will learn:
· What are spheres?
· Volume and surface area of spheres
· Application questions involving volume and surface area of spheres
What is a sphere?
Based on geometrical terms, A sphere is a three-dimensional geometrical object that is identical to a ball, and every point on its surface is equidistant (having the same distance) from its center.
The main dimension to know about a sphere is very simple: its radius. The radius of a sphere is measured from the center of the sphere to any point on the surface of the sphere.
How to find the volume of sphere?
The general formula to find the volume of a sphere is:
V = 4/3 π r^3
where V is the volume of the sphere and r is the radius of the sphere
How to find the surface area of spheres?
The general formula to find the total surface area of a sphere is:
Total Area = 4 π r^2
where r is the radius of the sphere
Application examples involving spheres
Finding the volume of a sphere
A ball bearing (which is spherical in shape) has a radius of 2.4 cm. Find
i) the volume of the ball bearing,
ii) the mass of 2500 identical ball bearings if they are made of wood of density 1.5 g/cm^3.
Solution:
i) Volume of ball bearing = 4/3 π r^3
= 4/3 x π x (2.4)^3
= 1.8432π cm^3
= 57.9 cm^3 (to 3 s.f.)
ii) Mass of 2500 ball bearings = volume of 2500 ball bearings × density
= 2500 × 18.432π × 1.5
= 217 000 g (to 3 s.f.)
Finding the total surface area of a sphere
A solid sphere has a diameter of 7.8 cm. Find its surface area.
Solution:
Radius of sphere = 7.8 ÷ 2
= 3.9 cm
Surface area of sphere = 4πr^2
= 4 × π × (3.9)^2
= 60.84π
= 191 cm^2 (to 3 s.f.)
And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on spheres, their formulae and its application!
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