Question

A globe company currently manufactures a globe that is 16 inches in diameter. If the dimensions of the globe were reduced by half, what would its volume be? Use 3. 14 for π and round your answer to the nearest tenth. 682. 7 in3 2143. 6 in3 85. 3 in3 267. 9 in3.

Answer 1

Volume is the space occupied by an object. The volume of the globe is 268.0825 in³.

What is the volume of a sphere?

The volume of the sphere is given by the formula,

$\text{Volume of Sphere}= \dfrac{4}{3} \pi r^3$

We know that the diameter of the globe is reduced to half, therefore, the diameter of the globe,

$\rm \text{New Diameter of the globe} = \dfrac{Diameter}{2} = \dfrac{16}{2} = 8\ inches$

Also, the radius of the globe is half of its diameter,

$\rm Radius = \dfrac{Diameter}{2} = \dfrac{8}{2} = 4\ inches$

We know that the shape of a globe is spherical, also, we know the formula of the volume of the sphere, therefore, the volume of the globe can be written as,

$\begin{aligned}\text{Volume of Globe}&= \dfrac{4}{3} \pi r^3\\\\& =\dfrac{4}{3} \pi (4)^3\\\\&=268.0825\rm\ in^3 \end{aligned}$

Hence, the volume of the globe is 268.0825 in³.

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