Exercise 42 Page 854

Use the formula for the surface area of a sphere and the formula for the volume of a sphere.

Surface area is 16 times larger, and the volume is 64 times larger.

Practice makes perfect

Let r be the radius of a sphere.

We are asked to describe how multiplying the radius of the sphere by 4 affects the surface area and the volume of the sphere. Therefore, the radius of the new sphere is r_\text{new}=4r.

Let's use the formula for the surface area of a sphere and the formula for the volume of a sphere.

Sphere	Old	New
Radius	r	4r
Area	A=4π Radius^2
Area	\textcolor{darkorange}{A_\text{old}}=\textcolor{darkorange}{4\pi r^2}	A_\text{new}=4\pi ({\color{#0000FF}{4r}})^2=16\cdot \textcolor{darkorange}{4\pi r^2}
Volume	V=4/3π Radius^3
Volume	\textcolor{darkviolet}{V_\text{old}}=\textcolor{darkviolet}{\dfrac{4}{3}\pi r^3}	V_\text{new}=\dfrac{4}{3}\pi ({\color{#0000FF}{4r}})^3=64\cdot\textcolor{darkviolet}{\dfrac{4}{3}\pi r^3}

From the table above we get that A_\text{new}=16\textcolor{darkorange}{A_\text{old}} and V_\text{new}=64\textcolor{darkviolet}{V_\text{old}}. This tells us that the surface area of the sphere is 16 times larger and the volume of the sphere is 64 times larger if we multiply the radius by 4.

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Exercises p.852-855

Exercise 42 Page 854

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