An ice-cream container is in the shape of a truncated cone. If its base is 13cm in diameter, its top is 14cm in diameter and its height is 15cm, find the capacity of the container to the nearest mL.
First, we need to find the radius of the base and the top of the truncated cone.
Radius of the base (r1) = 13cm / 2 = 6.5cm
Radius of the top (r2) = 14cm / 2 = 7cm
Next, we find the volume of the truncated cone using the formula:
V = 1/3 * π * h * (r1^2 + r2^2 + (r1 * r2))
V = 1/3 * π * 15cm * (6.5^2 + 7^2 + (6.5 * 7))
V = 1/3 * π * 15cm * (42.25 + 49 + 45.5)
V = 1/3 * π * 15cm * 136.75
V = 2261.25π cm^3
Finally, we convert the volume to mL by multiplying by 1mL/cm^3:
V ≈ 2261.25π * 1 ≈ 7108.81 mL
Therefore, the capacity of the ice-cream container is approximately 7108.81 mL.
The answer is 1406mL
Apologies for the mistake in the previous calculation. Let's correct it:
First, we calculate the radii of the base and the top of the truncated cone:
Radius of the base (r1) = 13 cm / 2 = 6.5 cm
Radius of the top (r2) = 14 cm / 2 = 7 cm
Next, we find the volume of the truncated cone using the formula:
V = 1/3 * π * h * (r1^2 + r2^2 + r1 * r2)
V = 1/3 * π * 15 cm * (6.5^2 + 7^2 + 6.5 * 7)
V = 1/3 * π * 15 cm * (42.25 + 49 + 45.5)
V = 1/3 * π * 15 cm * 136.75
V = 682.5π cm^3
Convert the volume to mL by multiplying by 1 mL/cm^3:
V ≈ 682.5π * 1 ≈ 2143.78 mL
Therefore, the capacity of the ice cream container is approximately 2143.78 mL.
Use this formula: 1/3(B + B' + square root of B × B') × h to find the answer
Sure! Let's use the formula you provided to find the capacity of the ice cream container.
Given:
Base diameter (B) = 13 cm
Top diameter (B') = 14 cm
Height (h) = 15 cm
Using the formula:
V = 1/3(B + B' + √(B * B')) * h
V = 1/3(13 + 14 + √(13 * 14)) * 15
V = 1/3(27 + 15.33) * 15
V = 1/3(42.33) * 15
V = 14.11 * 15
V = 211.65 cm^3
Converting to mL by multiplying by 1mL/cm^3:
V ≈ 211.65 mL
Therefore, the capacity of the ice-cream container is approximately 211.65 mL.