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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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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}}}

{\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

r= 3

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

Calculate power

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

Multiply fractions

V_\text{hemisphere}=\dfrac{4}{6}\cdot \pi (27)

a/b=.a /2./.b /2.

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

Multiply

V_\text{hemisphere}=\dfrac{2}{3}\cdot 27\pi

MoveRightFacToNum

a/c* b = a* b/c

V_\text{hemisphere}=\dfrac{2\cdot 27\pi}{3}

Multiply

V_\text{hemisphere}=\dfrac{54\pi}{3}

Calculate quotient

V_\text{hemisphere}=18\pi

Therefore, the volume of the hemisphere is 18π cubic centimeters.

Subchapter links

1 Representations of Three-Dimensional Figures p.872

2 Surface Areas of Prisms and Cylinders p.872

3 Surface Areas of Pyramids and Cones p.872

4 Volumes of Prisms and Cylinders p.873

5 Volumes of Pyramids and Cones p.873

6 Surface Areas and Volumes of Spheres p.873

7 Spherical Geometry p.874

8 Congruent and Similar Solids p.874