Question

find the volume of each of the following figures. complete parts (a) through (e) below
(type an exact answer in terms of π. use integers or
fractions for any numbers in the expression.)
b. right triangular prism
the volume is 448 cm³.
(type an exact answer in terms of π. use integers or
fractions for any numbers in the expression.)
c. right circular cone
the volume is
(type an exact answer in terms of π. use integers or
fractions for any numbers in the expression.)

Explanation:

Step1: Recall the formula for the volume of a cone

The volume formula for a right - circular cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height of the cone.

Step2: Identify the values of \(r\) and \(h\)

From the figure, the radius \(r = 5\space cm\) and the height \(h=6\space cm\).

Step3: Substitute the values into the formula

Substitute \(r = 5\) and \(h = 6\) into \(V=\frac{1}{3}\pi r^{2}h\).

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Answer:

\(50\pi\space cm^{3}\)