Question

1. which of the following geometric shapes have the same volume? select each shape that has the same volume. a. a sphere with a radius of 3 cm. b. a cylinder with a radius of 8 cm and a height of 11 cm. c. a hemisphere with a radius of 5 cm. d. a cone with a radius of 5 cm and a height of 10 cm. 6. a water tank in the form of a cylinder has a radius of 6 feet and a height of 32 feet. what is the volume of the water tank in cubic feet? (use π = 3.14) round the answer to two decimal places if necessary. 7. a sphere has a radius of 9 feet. what is the volume of the sphere in cubic feet? (use π = 3.14) round the answer to two decimal places if necessary.

Explanation:

Step1: Volume of cylinder formula

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 6\) feet and \(h=32\) feet, and \(\pi = 3.14\).

Step2: Substitute values into formula

Substitute \(r = 6\), \(h = 32\), and \(\pi=3.14\) into \(V=\pi r^{2}h\).

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Step3: Volume of sphere formula

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 9\) feet and \(\pi=3.14\).

Step4: Substitute values into formula

Substitute \(r = 9\) and \(\pi = 3.14\) into \(V=\frac{4}{3}\pi r^{3}\).

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Answer:

For question 6: \(3617.28\) cubic feet.
For question 7: \(3052.08\) cubic feet.