V=pir^(2)h The equation gives the Volume V of a right cylinder with radius r and height h. Which of the following equations correctly gives the radius of the cylinder in terms of the cylinder's volume and height? Choose 1 answer: (A) r=(sqrt(Vh))/(pi) (B) r=sqrt((Vh)/(pi)) (c) r=(sqrtV)/(pi h) (D) r=sqrt((V)/(pi h))

Question

V=pir^(2)h The equation gives the Volume  V of a right cylinder with radius  r and height  h. Which of the following equations correctly gives the radius of the cylinder in terms of the cylinder's volume and height? Choose 1 answer: (A)  r=(sqrt(Vh))/(pi) (B)  r=sqrt((Vh)/(pi)) (c)  r=(sqrtV)/(pi h) (D)  r=sqrt((V)/(pi h))

Bytelearn · Accepted Answer

Write Volume Formula: Write down the original volume formula for a right cylinder. The volume V of a right cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.Isolate r^2: Isolate the term r^2 in the volume formula. To find the radius r in terms of the volume V and height h, we need to isolate r^2. We do this by dividing both sides of the equation by πh. V = πr^2h => r^2 = V / (πh)Take Square Root: Take the square root of both sides to solve for r. To solve for r, we take the square root of both sides of the equation. r = sqrt(V / (πh))Verify Answer: Verify that the answer matches one of the given options. Comparing the derived formula r = sqrt(V / (πh)) with the given options, we find that it matches option (D).

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