QuestionCalculate the volume of a sphere with a diameter of 3 cm. Options: $3 \pi$ , $36 \pi$ , $\frac{9}{2} \pi$ , $\frac{9}{8} \pi$ .

Studdy Solution

STEP 1

Assumptions1. The sphere has a diameter of3 centimeters. . The formula for the volume of a sphere is given by $\frac{4}{3}\pi r^{3}$ , where $r$ is the radius of the sphere.

STEP 2

First, we need to find the radius of the sphere. The radius is half the diameter.
$r = \frac{iameter}{2}$

STEP 3

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{3\, cm}{2}$

STEP 4

Calculate the radius of the sphere.
$r = \frac{3\, cm}{2} =1.\, cm$

STEP 5

Now that we have the radius, we can find the volume of the sphere using the formula $\frac{4}{3}\pi r^{3}$ .
$Volume = \frac{4}{3}\pi r^{3}$

STEP 6

Plug in the value for the radius to calculate the volume.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3}$

STEP 7

Calculate the volume of the sphere.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3} = \frac{9}{2} \pi\, cm^{3}$ The volume of the sphere is $\frac{9}{2} \pi$ cubic centimeters.

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QuestionCalculate the volume of a sphere with a diameter of 3 cm. Options: $3 \pi$ , $36 \pi$ , $\frac{9}{2} \pi$ , $\frac{9}{8} \pi$ .

Studdy Solution

STEP 1

Assumptions1. The sphere has a diameter of3 centimeters. . The formula for the volume of a sphere is given by $\frac{4}{3}\pi r^{3}$ , where $r$ is the radius of the sphere.

STEP 2

First, we need to find the radius of the sphere. The radius is half the diameter.
$r = \frac{iameter}{2}$

STEP 3

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{3\, cm}{2}$

STEP 4

Calculate the radius of the sphere.
$r = \frac{3\, cm}{2} =1.\, cm$

STEP 5

Now that we have the radius, we can find the volume of the sphere using the formula $\frac{4}{3}\pi r^{3}$ .
$Volume = \frac{4}{3}\pi r^{3}$

STEP 6

Plug in the value for the radius to calculate the volume.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3}$

STEP 7

Calculate the volume of the sphere.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3} = \frac{9}{2} \pi\, cm^{3}$ The volume of the sphere is $\frac{9}{2} \pi$ cubic centimeters.

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QuestionCalculate the volume of a sphere with a diameter of 3 cm. Options: 3π3 \pi3π, 36π36 \pi36π, 92π\frac{9}{2} \pi29​π, 98π\frac{9}{8} \pi89​π.

Studdy Solution

STEP 1

Assumptions1. The sphere has a diameter of3 centimeters. . The formula for the volume of a sphere is given by 43πr3\frac{4}{3}\pi r^{3}34​πr3, where rrr is the radius of the sphere.

STEP 2

First, we need to find the radius of the sphere. The radius is half the diameter.r=iameter2r = \frac{iameter}{2}r=2iameter​

STEP 3

Now, plug in the given value for the diameter to calculate the radius.r=3 cm2r = \frac{3\, cm}{2}r=23cm​

STEP 4

Calculate the radius of the sphere.r=3 cm2=1. cmr = \frac{3\, cm}{2} =1.\, cmr=23cm​=1.cm

STEP 5

Now that we have the radius, we can find the volume of the sphere using the formula 43πr3\frac{4}{3}\pi r^{3}34​πr3.Volume=43πr3Volume = \frac{4}{3}\pi r^{3}Volume=34​πr3

STEP 6

Plug in the value for the radius to calculate the volume.Volume=43π(1.5 cm)3Volume = \frac{4}{3}\pi (1.5\, cm)^{3}Volume=34​π(1.5cm)3

STEP 7

Calculate the volume of the sphere.Volume=43π(1.5 cm)3=92π cm3Volume = \frac{4}{3}\pi (1.5\, cm)^{3} = \frac{9}{2} \pi\, cm^{3}Volume=34​π(1.5cm)3=29​πcm3The volume of the sphere is 92π\frac{9}{2} \pi29​π cubic centimeters.

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QuestionCalculate the volume of a sphere with a diameter of 3 cm. Options: $3 \pi$ , $36 \pi$ , $\frac{9}{2} \pi$ , $\frac{9}{8} \pi$ .

Assumptions1. The sphere has a diameter of3 centimeters. . The formula for the volume of a sphere is given by $\frac{4}{3}\pi r^{3}$ , where $r$ is the radius of the sphere.

First, we need to find the radius of the sphere. The radius is half the diameter.
$r = \frac{iameter}{2}$

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{3\, cm}{2}$

Calculate the radius of the sphere.
$r = \frac{3\, cm}{2} =1.\, cm$

Now that we have the radius, we can find the volume of the sphere using the formula $\frac{4}{3}\pi r^{3}$ .
$Volume = \frac{4}{3}\pi r^{3}$

Plug in the value for the radius to calculate the volume.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3}$

Calculate the volume of the sphere.
$Volume = \frac{4}{3}\pi (1.5\, cm)^{3} = \frac{9}{2} \pi\, cm^{3}$ The volume of the sphere is $\frac{9}{2} \pi$ cubic centimeters.