Applications of Area and Volume

The radius of a circle is increasing at a constant rate of 0.2 meters per second.  What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?

• 0.04π m²/sec

• 0.4π m²/sec

• 4π m²/sec

• 20π m²/sec

The radius of a sphere is decreasing at a rate of 2 cm/sec.  At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere?  (The surface area of a sphere is A = 4πr².)

• -108π

• -72π

• -48π

• -24π

A rectangular solid that has a square base has a surface area of 150 square inches.  Find the maximum volume of the solid.  (use Calculus)

• 5

• 125

• 150

• 250

Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square.

• 1.8 cm²

• 1.89 cm²

• 0.9 cm²

• 19.8 cm²

An open box is to be made from a 2-foot by 3-foot rectangular piece of material by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made in this manner.

• 0.392 ft³

• 2.683 ft³

• 1.056 ft³

• 0.4140 ft³

Find the volume of a rectangular prism with length (x+2), width (x-4), and height (2x+1).

Find the width for a rectangle that has an area of 2x² + 6x – 8 and length of 2x – 2

• x + 4

• 2x² + 4x – 6

• x - 4

• x + 4 - 16/(2x-2)

A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?

• 59.259 cm³

• 23.361 cm³

• 37.483 cm³

• 43.961 cm³

You want to create a garden in your backyard. Given are the dimensions of the garden and a border. Determine the area of the gray border surrounding the garden bed.

• 8x + 24

• 6x + 32

• 2x² - 8x + 4

• x² + 16x + 16

The length of your storage crate is 2 meters greater than its width, and its height is 1 meter greater than its width. If the volume if 24 cubic meters, find the width, length, and height.

• width = 2m

  length = 4m

  height = 3m

• width = 1m

  length = 6m

  height = 4m

• width = 2m

  length = 6m

  height = 2m

• width = 3m

  length = 4m

  height = 2m