4 cm, 5cm, 6 cm, 6cm, 14 cm
Solve for the volume of the composite figure.
448 cm^3
616 cm^3
154 cm^3
952 cm^3
To find the volume of the composite figure, we first need to find the total combined volume of all the individual shapes. Then we sum up the volumes to get the total volume.
1. Volume of the first cylinder with a radius of 4 cm and height of 14 cm:
V1 = πr^2h = π(4^2)(14) = 224π cm^3
2. Volume of the second cylinder with a radius of 5 cm and height of 6 cm:
V2 = πr^2h = π(5^2)(6) = 150π cm^3
3. Volume of the third cylinder with a radius of 6 cm and height of 6 cm:
V3 = πr^2h = π(6^2)(6) = 216π cm^3
Adding up the volumes of all three cylinders:
Total Volume = V1 + V2 + V3
Total Volume = 224π + 150π + 216π
Total Volume = 590π cm^3
Total Volume ≈ 1852.34 cm^3
Therefore, the volume of the composite figure is approximately 1852.34 cm^3. None of the given options match this result.
It has to be one of the answers
Apologies for the mistake in the previous calculation. Let's recalculate the volume of the composite figure with the given dimensions.
Given dimensions:
4 cm, 5 cm, 6 cm, 6 cm, 14 cm
Volume of the first cylinder with radius 4 cm and height 14 cm:
V1 = π(4^2)(14) = 224π cm^3
Volume of the second cylinder with radius 5 cm and height 6 cm:
V2 = π(5^2)(6) = 150π cm^3
Volume of the third cylinder with radius 6 cm and height 6 cm:
V3 = π(6^2)(6) = 216π cm^3
Total volume of the composite figure:
Total Volume = V1 + V2 + V3
Total Volume = 224π + 150π + 216π
Total Volume = 590π cm^3
Now, we need to convert this into a numerical value:
Total Volume ≈ 1852.34 cm^3
Therefore, the correct volume of the composite figure is approximately 1852.34 cm^3. Since none of the given options match this result, there was likely an error in the options provided.
PICK ONE OF THE ANSWERS ITS HAS TO BE ONE OF THE ANSWERS
Apologies for the oversight. Let's compare the total volume calculated to the given answer choices:
Total Volume = 590π cm^3
Total Volume ≈ 1852.34 cm^3
Out of the provided options, the closest answer to 1852.34 cm^3 is 952 cm^3.
Therefore, the closest match to the calculated total volume of the composite figure is 952 cm^3.