The volume of ice-cream in the cone is half the
volume of the cone. The cone has a 3 cm radius and
height of 14 cm. What is the depth of the ice-cream,
correct to 2 decimal places?
Answer = 11.11
since the volume is proportional to the cube of the linear dimensions, the new h is 14/∛2 = 11.11
To find the depth of the ice-cream in the cone, we need to determine the volume of the cone and then calculate half of that volume.
First, let's find the volume of the cone using the formula:
V = (1/3)πr²h
Given:
Radius (r) = 3 cm
Height (h) = 14 cm
Plugging in the values into the formula:
V = (1/3)π(3²)(14)
V = (1/3)π(9)(14)
V = (1/3)π(126)
V ≈ 132.73 cm³
Now, we need to find half of the volume of the cone:
V_ice-cream = (1/2) × V
V_ice-cream = (1/2) × 132.73
V_ice-cream ≈ 66.36 cm³
Since the ice-cream is in the shape of a cone, we can use the same formula to find its depth, but this time we'll be given the volume (V_ice-cream) and the radius (r_ice-cream).
Let's rearrange the formula for the volume of a cone to solve for height (h):
V_ice-cream = (1/3)πr_ice-cream²h_ice-cream
Now we can plug in the values we have:
66.36 = (1/3)πr_ice-cream²h_ice-cream
r_ice-cream = 3 cm
Substituting the radius in, we have:
66.36 = (1/3)π(3²)h_ice-cream
h_ice-cream = (66.36 × 3)/(9π)
h_ice-cream ≈ 7.37 cm
Therefore, the depth of the ice-cream in the cone is approximately 7.37 cm when rounded to 2 decimal places.