## Related questions with answers

Find the inner surface area A of a cylindrical 250.0 cubic cm cup as a function of the radius r of the base. Then if A = 175.0 square cm, solve for r. Write one or two paragraphs explaining your method for setting up the function, and how you used a graphing calculator to solve for r with the given value of A.

Solution

VerifiedIt is given that the volume of the cylindrical cup is 250 cm$^3$. The volume of a cylinder is $V=\pi r^2h$ so $\pi r^2h=250$. Solving this for $h$ gives $h=\dfrac{250}{\pi r^2}$. The surface area of a cylinder is $A=2\pi r^2+2\pi rh$. A cup only has one base though since the top is open so the surface area of the cup is $A=\pi r^2+2\pi rh$. Substituting in $h=\dfrac{250}{\pi r^2}$ then gives $A=\pi r^2+2\pi r\left(\dfrac{250}{\pi r^2}\right)=\pi r^2+\dfrac{500}{r}$.

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Basic Technical Mathematics with Calculus

10th Edition•ISBN: 9780133253528Allyn J. Washington#### Thomas' Calculus

14th Edition•ISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (5 more)James Stewart#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson## More related questions

- anatomy and physiology

1/4

- anatomy and physiology

1/7