Question

A punch bowl is in the shape of a hemisphere​ (half of a​ sphere) with a radius of 10 inches. The cup part of a ladle is also in the shape of a hemisphere with a radius of 6 inches. If the bowl is​ full, how many full ladles of punch are there in the​ bowl?

Answer 1

Answer:

There are 4 full ladles of punch in the bowl.

Step-by-step explanation:

Given the radius ''R'' the volume of a sphere is :

$V=\frac{4}{3}(\pi)R^{3}$

Therefore, the volume of half of a sphere is :

$V(HalfOfASphere)=\frac{V(Sphere)}{2}$

$V(HalfOfASphere)=\frac{2}{3}(\pi)R^{3}$

Let's start calculating the volume of the punch bowl (inches = in) :

$V(PunchBowl)=\frac{2}{3}(\pi)(10in)^{3}=\frac{2000}{3}(\pi)in^{3}$

Now we calculate the volume of the cup part of the ladle :

$V(Ladle)=\frac{2}{3}(\pi)(6in)^{3}=144(\pi)in^{3}$

Finally we divide the volume of the punch bowl by the volume of the ladle

$\frac{V(PunchBowl)}{V(Ladle)}=\frac{\frac{2000}{3}(\pi)in^{3}}{144(\pi)in^{3}}=4.63$

They are 4.63 ladles in the punch bowl. Therefore, there are 4 full ladles of punch in the bowl.