A cone has a radius of 24 cm and volume of 1,920 cm3 What is the volume of a similar cone with a radius of 18 cm
1. 480 cm3
2. 810 cm3
3. 1,080 cm3
4. 1,440 cm3
explain why
The formula for the volume of a cone is V = 1/3πr²h, where r is the radius and h is the height.
We know the radius of the first cone is 24 cm and the volume is 1,920 cm3, so we can use this to find the height:
1,920 = 1/3π(24²)h
Solving for h, we get h = 5 cm
Now, we can use the formula for the volume of a cone again, but with the new radius of 18 cm and the same height of 5 cm:
V = 1/3π(18²)(5)
V ≈ 810 cm3
Therefore, the answer is 2. 810 cm3.
To find the volume of a similar cone, we can use the ratio of the radii of the two cones raised to the power of 3 as a scaling factor.
In this case, the ratio of the radii is 18 cm / 24 cm = 3/4.
Therefore, the volume of the similar cone can be found by multiplying the volume of the original cone by the scaling factor (3/4) raised to the power of 3:
Volume of similar cone = (Volume of original cone) * [(radius of similar cone) / (radius of original cone)]^3
= 1,920 cm^3 * (18 cm / 24 cm)^3
= 1,920 cm^3 * (3/4)^3
≈ 1,080 cm^3
So, the correct answer is 3. 1,080 cm^3.