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Angelina_Jolie [31]
2 years ago
12

Match each spherical volume to the largest cross sectional area of that sphere

Mathematics
2 answers:
zlopas [31]2 years ago
5 0

Answer:

Part 1) 324\pi\ units^{2} ------> 7,776\pi\ units^{3}

Part 2) 36\pi\ units^{2} ------> 288\pi\ units^{3}

Part 3) 81\pi\ units^{2} ------> 972\pi\ units^{3}

Part 4) 144\pi\ units^{2} ------> 2,304\pi\ units^{3}

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

A=324\pi\ units^{2}

The area of the circle is equal to

A=\pi r^{2}

so

324\pi=\pi r^{2}

Solve for r

r^{2}=324

r=18\ units

Find the volume of the sphere

The volume of the sphere is

V=\frac{4}{3}\pi r^{3}

For r=18\ units

substitute

V=\frac{4}{3}\pi (18)^{3}

V=7,776\pi\ units^{3}

Part 2) we have

A=36\pi\ units^{2}

The area of the circle is equal to

A=\pi r^{2}

so

36\pi=\pi r^{2}

Solve for r

r^{2}=36

r=6\ units

Find the volume of the sphere

The volume of the sphere is

V=\frac{4}{3}\pi r^{3}

For r=6\ units

substitute

V=\frac{4}{3}\pi (6)^{3}

V=288\pi\ units^{3}

Part 3) we have

A=81\pi\ units^{2}

The area of the circle is equal to

A=\pi r^{2}

so

81\pi=\pi r^{2}

Solve for r

r^{2}=81

r=9\ units

Find the volume of the sphere

The volume of the sphere is

V=\frac{4}{3}\pi r^{3}

For r=9\ units

substitute

V=\frac{4}{3}\pi (9)^{3}

V=972\pi\ units^{3}

Part 4) we have

A=144\pi\ units^{2}

The area of the circle is equal to

A=\pi r^{2}

so

144\pi=\pi r^{2}

Solve for r

r^{2}=144

r=12\ units

Find the volume of the sphere

The volume of the sphere is

V=\frac{4}{3}\pi r^{3}

For r=12\ units

substitute

V=\frac{4}{3}\pi (12)^{3}

V=2,304\pi\ units^{3}

Katarina [22]2 years ago
4 0

Answer:

grilled cheese prolly

Step-by-step explanation:

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An object is 3.6 m from the pinhole. Its image is 4.2 cm from the opposite side of the pinhole. The height of the image is 0.8 c
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From the given question;

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Explain whether the points (-13,4), (-7,3), (-1,2), (5,1). (11,0), (17, -1) represent the set of all the solutions for the
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Step-by-step explanation:

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Greg has 4 shirts: a white one, a black one, a red one, and a blue one. He also has two pairs of pants, one blue and one tan. Wh
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The distribution of the pants and the shirts illustrates probability

The probability that he winds up wearing the white shirt and tan pants is 1/8

<h3>How to determine the probability?</h3>

The number of shirts is given as:

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The number of pants is given as:

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The probability that he winds up wearing the white shirt and tan pants is then calculated as:

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