Video: Finding the Volume of a Sphere

Work out the volume of the sphere, giving your answer accurate to two decimal places.

01:38

Video Transcript

Work out the volume of the sphere, giving your answer accurate to two decimal places.

First, we remember the formula we need for calculating the volume of a sphere. It’s four-thirds 𝜋𝑟 cubed, where 𝑟 is the radius of the sphere. We can see from the diagram that the radius of this sphere is 6.3 centimeters. That’s the distance from any point on the sphere’s surface to the center of the sphere. So we can substitute this value of 𝑟 directly into our formula, giving that the volume of this sphere is equal to four-thirds 𝜋 multiplied by 6.3 cubed.

We must remember that it is only the radius that we are cubing, so only the value of 6.3, not the factors of four-thirds and 𝜋. As we’ve been asked to give our answer accurate to two decimal places, it’s reasonable to assume that we can use a calculator. So evaluating this on our calculators gives 1047.394424 continuing.

In order to round our answer to two decimal places, we need to consider the value in the third decimal place. It is a four. And as this is less than five, this tells us that we’re rounding down. So we have a value of 1047.39. The units of volume will be cubic units. And as the units given for the radius were centimeters, the units for the volume will be cubic centimeters. And so we have our answer to this problem. The volume of the sphere, given to two decimal places, is 1047.39 cubic centimeters.

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