An ice-cream container is in the shape of a truncated cone. If it's base is 13cm in diameter, it's top is 14cm in diameter and it's height is 15cm find the capacity of the container to the nearest ml
To find the capacity of the ice-cream container, we first need to find the volume of the truncated cone.
The formula for the volume of a truncated cone is given by:
V = 1/3 * π * h * (r1^2 + r2^2 + r1 * r2)
where h is the height of the cone, r1 is the radius of the base, and r2 is the radius of the top.
Given:
h = 15cm
r1 = 6.5cm (radius = diameter / 2)
r2 = 7cm
Substitute these values into the formula:
V = 1/3 * π * 15 * (6.5^2 + 7^2 + 6.5 * 7)
V = 1/3 * π * 15 * (42.25 + 49 + 45.5)
V = 1/3 * π * 15 * 136.75
V ≈ 2276.11 cm^3
Finally, convert the volume to mL:
1 cm^3 = 1 mL
Therefore, the capacity of the ice-cream container is approximately 2276 mL.