Question

Two spherical pieces of cookie dough have radii of 3cm & 5cm. The pieces are combined to form one large spherical piece of dough. What is the approximate radius of the new sphere of dough?

Answer 1

The traffic cone is 19 inches tall & has a radius of 5 inches. Find the lateral area.

Answer 2

You'll need to find the volume of the first two balls of dough. The combined ball will have the sum of the two volumes.
\[V_1=\frac{4}{3}\pi (3)^3=36\pi~~~~\text{and}~~~~V_2=\frac{4}{3}\pi (5)^3=\frac{500}{3}\pi\]
so the third ball would have volume \(V_3=\dfrac{608}{3}\pi\).

Solve for the third ball's radius:
\[\frac{608}{3}\pi=\frac{4}{3}\pi r^3~~\iff~~152=r^3~~\iff~~r\approx5.337\]

Answer 3

The traffic cone is 19 inches tall & has a radius of 5 inches. Find the lateral area.