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.
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.
5 answers
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.
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.
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.