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McGraw Hill Integrated II, 2012 View details

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Exercise 30 Page 873

Use the formula for the volume of a sphere.

18π cubic centimeters

Practice makes perfect

Cement is poured into the following hemisphere with a diameter of 6 centimeters.

Since the radius is half of the diameter, we get that it is equal to r= 62= 3 centimeters. We are asked to find the volume of the hemisphere, V_\text{hemisphere}. Let's use the formula for the volume of a sphere.

V_\text{hemisphere}=\dfrac{1}{2}\cdot {\color{#FF0000}{V_\text{sphere}}}

Substitute

{\color{#FF0000}{V_\text{sphere}}}={\color{#0000FF}{{\color{#FF0000}{\dfrac{4}{3}\pi r^3}}}}

V_\text{hemisphere}=\dfrac{1}{2}\cdot {\color{#FF0000}{\dfrac{4}{3}\pi r^3}}

▼

Substitute 3 for r and evaluate

Substitute

r= 3

V_\text{hemisphere}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi ({\color{#0000FF}{3}})^3

CalcPow

Calculate power

V_\text{hemisphere}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi (27)