An ice cream server fills a cone, which is 15.7 cm high and 7.2 cm across, with ice cream. She then tops the cone with a nicely rounded half-scoop. On top of this she puts the second scoop. To the nearest cubic centimeter, how much ice cream did you receive?
The way I interpret the question:
The first scoop on the top is a half scoop, the second scoop is a full scoop ?
If the second scoop is also a half-scoop, then change the 3/2 to 1
you would have the volume of the cone + (3/2) spheres
vol = (1/3)π(3.6)^2 (15.7) + 2(4/3)π(3.6)^3
= ....
(your turn)
To calculate the volume of the ice cream in the cone, we need to find the volume of the cone and the volume of the two scoops.
Volume of the cone:
The formula to find the volume of a cone is:
Vcone = (1/3) * π * r² * h
where r is the radius and h is the height.
Given:
Height of the cone (h) = 15.7 cm
Radius of the cone (r) = half of the diameter = 7.2 cm / 2 = 3.6 cm
Plugging the values into the formula:
Vcone = (1/3) * π * (3.6 cm)² * 15.7 cm
Calculating the volume of the cone will give us the volume of ice cream underneath the two scoops.
Now let's calculate the volume of a half-scoop of ice cream:
Assuming the half-scoop is in the shape of a hemisphere,
the formula to find the volume of a hemisphere is:
Vhemisphere = (2/3) * π * r³
Given:
Radius of the half-scoop (r) = 3.6 cm
Plugging the value into the formula:
Vhemisphere = (2/3) * π * (3.6 cm)³
Finally, let's calculate the volume of the second scoop, assuming it's a full sphere:
The formula to find the volume of a sphere is:
Vsphere = (4/3) * π * r³
Given:
Radius of the second scoop (r) = 3.6 cm
Plugging the value into the formula:
Vsphere = (4/3) * π * (3.6 cm)³
To find the total volume of ice cream received, we need to find the sum of the cone volume, the half-scoop volume, and the second scoop volume.
Total volume = Vcone + Vhemisphere + Vsphere
Now we can plug in the values we calculated and evaluate the expression to find the answer.