Solve the problem.
-A can has a surface area of 970 square inches. Its height is $5.34$ inches. What is the radius of the circular top? Round to the nearest hundredth.
A) $10.04 \mathrm { in }$.
B) $13.03$ in.
C) $28.91 \mathrm { in }$.
D) $4.93 \mathrm { in }$.

Question

Quizplus · Accepted Answer

The surface area of a cylinder is given by the formula $2\pi r^2 + 2\pi rh$, where $r$ is the radius and $h$ is the height. Given the surface area $970$ square inches and height $5.34$ inches, we can solve for $r$. Rearranging the formula to solve for $r$, we get $r = \sqrt{\frac{970 - 2\pi(5.34)r}{2\pi}}$. However, to simplify, we recognize that the formula includes both the area of the two circles ($2\pi r^2$) and the area of the side ($2\pi rh$). We can isolate the side area part by subtracting it from the total surface area: $970 - 2\pi(5.34)r$, but this step involves recognizing that we directly don't solve for $r$ this way but rather understand the components of the surface area. The correct approach involves recognizing that the surface area consists of two parts: the area of the two circles ($2\pi r^2$) and the area of the side ($2\pi rh$). Given the total surface area and the height, we can use these to find the radius. First, find the area of the side: $2\pi rh = 2\pi(5.34)r$, and subtract this from the total surface area to find the area of the two circles. However, the direct calculation from the given information involves understanding that the total surface area includes the area of the sides and the tops/bottoms. By setting up the equation based on the total surface area and solving for $r$, we find that the radius that fits the given surface area and height is approximately $10.04$ inches, which corresponds to choice A. This involves algebraic manipulation and understanding of the geometry of cylinders.

Solve the Problem 5.345.345.34 Inches What Is the Radius of the Circular Top? Round

Solve the Problem $5.34$ Inches What Is the Radius of the Circular Top? Round