Question

A cylinder has a height of 10 feet. Its volume is 10,173.6 cubic feet. What is the radius of the cylinder?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

9. A triangular pyramid has a base shaped like a right triangle. The legs of the right triangle are 8 and 8 centimeters long. The pyramid's height is 12 centimeters. What is its volume?

Note: The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid
*
2 points
768 cubic centimeters
96 cubic centimeters
384 cubic centimeters
128 cubic centimeters

Answer 2

To find the radius of the cylinder, we first need to calculate the formula for the volume of a cylinder:

Volume of a cylinder = πr^2h

Given that the volume of the cylinder is 10,173.6 cubic feet and the height is 10 feet, we can plug in these values and the approximation of π to solve for the radius:

10,173.6 = 3.14r^2(10)
r^2 = 10,173.6/(3.14*10)
r^2 = 323.56
r = √323.56
r ≈ 18.0

Therefore, the radius of the cylinder is approximately 18.0 feet.

Answer 3

First, we need to calculate the area of the right triangle base. Since the legs are both 8 cm, the area of the base can be calculated as:

Area = 0.5 * base * height = 0.5 * 8 * 8 = 32 square centimeters

Now, we can use the formula provided to find the volume of the triangular pyramid:

V = 1/3 * A * H = 1/3 * 32 * 12 = 128 cubic centimeters

Therefore, the volume of the triangular pyramid is 128 cubic centimeters.