A new metal cylindrical storage tank is to be made. If its volume is to be $2,5\bar00$ ft ³, what is the height of the tank if its radius is 7 ft? What is its total surface area? Round your answers to three significant digits. A) The height is 785 ft, the total surface area is 7,130 ft ². B) The height is 16.2 ft, the total surface area is 1,020 ft ². C) The height is 78.5 ft, the total surface area is 713 ft ². D) The height is 16.2 ft, the total surface area is 7,130 ft ². E) The height is 78.5 ft, the total surface area is 1,020 ft ².

Question

Quizplus · Accepted Answer

The volume of a cylinder is given by $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height. Given $V = 2,500$ ft$^3$ and $r = 7$ ft, solving for $h$ gives $h \approx 16.2$ ft. The total surface area of a cylinder is $A = 2\pi r^2 + 2\pi rh$, substituting $r = 7$ ft and $h \approx 16.2$ ft gives $A \approx 1,020$ ft$^2$.

A New Metal Cylindrical Storage Tank Is to Be Made 2,50ˉ02,5\bar002,50ˉ0

A New Metal Cylindrical Storage Tank Is to Be Made $2,5\bar00$