Question

find the volume of each of the following figures. complete parts (a) through (e) below

a. right circular cone with hemisphere

the volume is $\frac{575\pi}{3}cm^{3}$

(type an exact answer in terms of $\pi$. use integers or

fractions for any numbers in the expression.)

b. right triangular prism

the volume is

(type an exact ans

fractions for any nu

ression.)

Explanation:

Step1: Find the area of the triangular base

The formula for the area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base and height of the right - angled triangle are both \(8\) cm. So, $A = \frac{1}{2}\times8\times8=32$ \(cm^{2}\).

Step2: Calculate the volume of the prism

The formula for the volume of a prism is \(V=A\times h\), where \(A\) is the area of the base and \(h\) is the height (or length) of the prism. The length of the prism is \(14\) cm. So, \(V = 32\times14=448\) \(cm^{3}\).

Answer:

\(448\) \(cm^{3}\)