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?
Accepted Solution
A:
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 :[tex]V=\frac{4}{3}(\pi)R^{3}[/tex]Therefore, the volume of half of a sphere is :[tex]V(HalfOfASphere)=\frac{V(Sphere)}{2}[/tex][tex]V(HalfOfASphere)=\frac{2}{3}(\pi)R^{3}[/tex]Let's start calculating the volume of the punch bowl (inches = in) :[tex]V(PunchBowl)=\frac{2}{3}(\pi)(10in)^{3}=\frac{2000}{3}(\pi)in^{3}[/tex]Now we calculate the volume of the cup part of the ladle :[tex]V(Ladle)=\frac{2}{3}(\pi)(6in)^{3}=144(\pi)in^{3}[/tex]Finally we divide the volume of the punch bowl by the volume of the ladle [tex]\frac{V(PunchBowl)}{V(Ladle)}=\frac{\frac{2000}{3}(\pi)in^{3}}{144(\pi)in^{3}}=4.63[/tex]They are 4.63 ladles in the punch bowl. Therefore, there are 4 full ladles of punch in the bowl.