Multiple choice

A cylinder has a total surface area of 616 cm², and the height is equal to the radius. Find the volume of the cylinder.

  1. 980 cm³

  2. 1078 cm³

  3. 990 cm³

  4. 1080 cm³

  5. 1120 cm³
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B Correct answer
Explanation

Total surface area of a cylinder is 2*pi*r*h + 2*pi*r^2. Given h=r, this becomes 2*pi*r^2 + 2*pi*r^2 = 4*pi*r^2. Setting 4*pi*r^2 = 616, we find r^2 = 616 / (4*pi) approx 49, so r=7. Volume = pi*r^2*h = pi*r^3 = pi*343 approx 1078.

AI explanation

Using the total surface area formula for a cylinder, 2 times pi times radius times the sum of radius and height, and knowing height equals radius, we set up the equation 616 equals 2 times pi times radius times 2 times radius. This simplifies to 616 equals 4 times pi times radius squared, meaning radius squared is 49 and the radius is 7 centimeters. Since the height is also 7 centimeters, the volume is pi times radius squared times height, yielding pi times 49 times 7, which equals 1078 cubic centimeters.

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