Video: Finding the Radius of a Sphere Given its Volume

A sphere has a volume of 630 cm³. Find the radius of the sphere to two decimal places.

02:15

Video Transcript

A sphere has a volume of 630 cubic centimeters. Find the radius of the sphere to two decimal places.

To calculate the volume of any sphere, we can use the formula four-thirds 𝜋𝑟 cubed. In this question, we are told the volume and need to calculate the radius. We could start by rearranging the formula to make 𝑟 the subject. Alternatively, we can substitute in our values and then use the balancing method to calculate the value of 𝑟.

We will use this method. So, we begin with 630 is equal to four-thirds 𝜋𝑟 cubed. We begin by dividing both sides of the equation by four-thirds. This is the same as multiplying by three-quarters. 630 multiplied by three-quarters is 472.5. The right-hand side simplifies to 𝜋𝑟 cubed.

Our next step is to divide both sides of the equation by 𝜋. The right-hand side simplifies to 𝑟 cubed. We could work out the left-hand side on the calculator. However, in the interest of accuracy, we will leave it as 472.5 divided by 𝜋. The opposite or inverse of cubing a number is cube rooting. So to calculate the value of 𝑟, we need to cube-root both sides of the equation.

𝑟 is equal to the cube root of 472.5 divided by 𝜋. Typing this into the calculator gives us 5.3180 and so on. As we need to round our answer to two decimal places, the eight in the thousandths column is the deciding number. If a deciding number is five or greater, we round up. The radius of the sphere, to two decimal places, is 5.32 centimeters.

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