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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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Answer:

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Step-by-step explanation:

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