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McGraw Hill Integrated II, 2012 View details

5. Volumes of Pyramids and Cones

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Exercise 26 Page 845

Use the formula for the volume of a cone.

About 471.2 cubic inches

Practice makes perfect

Let's analyze the given composite solid.

It consists of two solids.

A left cone with a radius of r= 5 inches and a height of h_1= 7 inches,
A right cone with a radius of r= 5 inches and a height of h_2= 11 inches.

Now, let's use the formula for the volume of a cone.

Solid	Left Cone	Right Cone
Radius	r= 5	r= 5
Height	h_1= 7	h_2= 11
Volume	V_\text{left}=\dfrac{1}{3}\pi {\color{#0000FF}{r}}^2{\color{#009600}{h_1}}	V_\text{right}=\dfrac{1}{3}\pi {\color{#0000FF}{r}}^2{\color{#009600}{h_2}}
Volume	\textcolor{darkorange}{V_\text{left}}=\dfrac{1}{3}\pi({\color{#0000FF}{5}})^2({\color{#009600}{7}})=\textcolor{darkorange}{\dfrac{175\pi}{3}}	\textcolor{darkviolet}{V_\text{right}}=\dfrac{1}{3}\pi ({\color{#0000FF}{5}})^2({\color{#009600}{11}})=\textcolor{darkviolet}{\dfrac{275\pi}{3}}

To find the volume of the composite solid we will add the volume of the cones. Then we will round our answer to the nearest tenth.

V_\text{solid}=\textcolor{darkorange}{V_\text{left}}+\textcolor{darkviolet}{V_\text{right}}

▼

Substitute values and evaluate

SubstituteII

\textcolor{darkorange}{V_\text{left}}={\color{#0000FF}{\textcolor{darkorange}{\dfrac{175\pi}{3}}}}, \textcolor{darkviolet}{V_\text{right}}={\color{#009600}{\textcolor{darkviolet}{\dfrac{275\pi}{3}}}}

V_\text{solid}=\textcolor{darkorange}{\dfrac{175\pi}{3}}+\textcolor{darkviolet}{\dfrac{275\pi}{3}}

AddFrac

Add fractions

V_\text{solid}=\dfrac{450\pi}{3}

CalcQuot

Calculate quotient

V_\text{solid}=150\pi

π ≈ 3.1416

V_\text{solid}\approx 150({\color{#0000FF}{3.1416}})

Multiply

V_\text{solid}\approx 471.24

RoundDec