Ice cream cone: cone + hemisphere
Here's a fun one — an ice cream cone! A scoop sits on top shaped like a hemisphere. What's the total volume?
We can break this into two shapes we already know — a hemisphere on top and a cone underneath.
Both shapes share the same radius — three centimeters. The cone is eight centimeters tall.
Start with the cone. Its volume is one-third times pi times r-squared times h.
Plug in our numbers: one-third times pi times three squared times eight.
Three squared is nine, times eight is seventy-two, times one-third is twenty-four. So the cone is twenty-four pi cubic centimeters.
Now the hemisphere. A whole sphere is four-thirds pi r-cubed, so half a sphere is two-thirds pi r-cubed.
Plug in: two-thirds times pi times three cubed.
Three cubed is twenty-seven, times two-thirds is eighteen. So the scoop is eighteen pi cubic centimeters.
To get the total, just add the two pieces: twenty-four pi plus eighteen pi is forty-two pi.
Multiplying by pi, forty-two pi is about one hundred thirty-one point nine.
The ice cream cone holds about one hundred thirty-two cubic centimeters. Nice work — break a tricky shape into easy ones!