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V=(4)/(3)pir^(3)
The formula gives the volume
V of a sphere with radius
r. If the volume of a sphere with a radius of 3 centimeters
k pi cubic centimeters, what is the value of
k ?

$V=\frac{4}{3} \pi r^{3}$ $\newline$ The formula gives the volume $V$ of a sphere with radius $r$ . If the volume of a sphere with a radius of $3$ centimeters $k \pi$ cubic centimeters, what is the value of $k$ ?

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q.

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

\newline

The formula gives the volume

V

of a sphere with radius

r

. If the volume of a sphere with a radius of

3

centimeters

k \pi

cubic centimeters, what is the value of

k

?

Identify Given Formula: Identify the given formula and the known values. $\newline$ The formula for the volume of a sphere is given by $V = \frac{4}{3}\pi r^3$ . We are given that the radius $r$ is $3$ centimeters.
Substitute Known Value: Substitute the known value of the radius into the formula. $\newline$ $V = \frac{4}{3}\pi(3 \, \text{cm})^3$
Calculate Volume: Calculate the volume using the substituted values. $\newline$ $V = \frac{4}{3}\pi(3^3) \, \text{cm}^3$ $\newline$ $V = \frac{4}{3}\pi(27) \, \text{cm}^3$
Simplify Expression: Simplify the expression to find the volume in terms of $\pi$ . $V = \frac{4}{3} \times 27\pi \, \text{cm}^3$ $V = 4 \times 9\pi \, \text{cm}^3$ $V = 36\pi \, \text{cm}^3$
Compare Calculated Volume: Compare the calculated volume with the given form $k\pi$ cubic centimeters. $\newline$ We have $V = 36\pi \, \text{cm}^3$ , which is in the form of $k\pi \, \text{cm}^3$ . Therefore, $k = 36$ .

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