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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 18 Page 875

Use the formula for the volume of a sphere.

About 5.3 centimeters

Two spherical pieces of cookie dough have radii of 3 cm and 5 cm, respectively.

We combine them into one large spherical piece of dough. Therefore, the volume of the large piece is equal to the sum of the volumes of two initial pieces. Let's find their volumes.

Sphere	Small 1	Small 2
Radius	r= 3	r= 5
Volume	V=4/3π r^3
Volume	V_1=4/3π( 3)^3=36π	V_2=4/3π( 5)^3=500π/3

Let's find the volume of the large piece of dough, V_\text{large}.

V_\text{large}=\textcolor{darkorange}{V_1}+\textcolor{darkviolet}{V_2}

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Substitute values and evaluate

V_1= 36π, V_2= 500π/3

V_\text{large}=\textcolor{darkorange}{36\pi}+\textcolor{darkviolet}{\dfrac{500\pi}{3}}

a = 3* a/3

V_\text{large}=\dfrac{3\cdot 36\pi}{3}+\dfrac{500\pi}{3}

Multiply

V_\text{large}=\dfrac{108\pi}{3}+\dfrac{500\pi}{3}

Add fractions

V_\text{large}=\dfrac{608\pi}{3}

Now, let's find the radius of the large sphere using the formula for the volume of a sphere again.

V_\text{large}=\dfrac{4}{3}\pi r^3

V_\text{large}={\color{#0000FF}{\dfrac{608\pi}{3}}}

608π/3=4/3π r^3

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Solve for r

LHS * 3=RHS* 3

608π =4π r^3

.LHS /π.=.RHS /π.

608=4 r^3

.LHS /4.=.RHS /4.

152=r^3

Rearrange equation

r^3=152

sqrt(LHS)=sqrt(RHS)

r=sqrt(152)

Use a calculator

r=5.336803...

Round to 1 decimal place(s)

r≈ 5.3

The radius of the large piece of dough is about 5.3 centimeters.