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Using the formula for the surface of a hemisphere $A = 3\pi r^2$ , what is the radius of the sphere if the area is $18.75\pi\,\text{cm}^2$ ?

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Convert equations of circles from general to standard form

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Q. Using the formula for the surface of a hemisphere

A = 3\pi r^2

, what is the radius of the sphere if the area is

18.75\pi\,\text{cm}^2

?

Write Formula: Write down the formula for the surface area of a hemisphere. $\newline$ The formula for the surface area of a hemisphere is $A = 3\pi r^2$ , where $A$ is the surface area and $r$ is the radius of the hemisphere.
Substitute Surface Area: Substitute the given surface area into the formula. $\newline$ We are given that the surface area $A$ is $18.75\pi$ cm $^2$ . So we substitute this value into the formula: $\newline$ $18.75\pi = 3\pi r^2$
Solve for $r^2$ : Solve for $r^2$ . To find $r^2$ , we need to divide both sides of the equation by $3\pi$ : $(18.75\pi) / (3\pi) = (3\pi r^2) / (3\pi)$ $r^2 = 18.75 / 3$
Calculate $r^2$ : Calculate the value of $r^2$ . Now we perform the division to find $r^2$ : $r^2 = \frac{18.75}{3}$ $r^\(2\) = \(6\).\(25\)
Find \(r\): Find the value of \(r\) by taking the square root of \(r^2\).\(\newline\)To find \(r\), we take the square root of both sides of the equation:\(\newline\)\(r = \sqrt{6.25}\)\(\newline\)\(r = 2.5\) cm

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