Question

The cylinder and rectangular prism below both have a height of 9 inches and a volume of 452.39in^3.

a. What is the area of the base of each object?

b. What is the radius of the cylinder?

c. If the rectangular prism has a width of 5.8 inches what is it's length?

Answer 1

a) Area of base of cylinder =
`=50.0346 in^2`

Area of base of prism = 50.265 sq.in.

b)Radius of cylinder = 3.99 in

c)If the rectangular prism has a width of 5.8 inches so. length is 8.66 in

Explanation:

Volume of cylinder =
`\pi r^2 h`

Height of cylinder = 9 inches

We are given that the volume of cylinder is
`452.39 in^3.`

`\pi r^2 h =452.39\\(22)/(7) r^2(9)=452.39\\r=\sqrt{(452.39 * 7)/(22* 9)}\\r=3.99`

Area of base of cylinder =
`\pi r^2= (22)/(7) * (3.99)^2=50.0346 in^2`

Volume of prism =
`Length * Breadth * height`

Height of prism = 9 inches

Volume of prism =
`452.39 in^3`

So,
`Length * Breadth * height =452.39`

`Length * Breadth * 9=452.39\\ Length * Breadth =(452.39)/(9)`

Area of base of prism = 50.265

Width of prism = 5.8

So,
`Length * 5.8 * 9 =452.39\\Length = (452.39)/(5.8 * 9 )\\Length =8.66647`

a) Area of base of cylinder =
`=50.0346 in^2`

Area of base of prism = 50.265

b)Radius of cylinder = 3.99 in

c)If the rectangular prism has a width of 5.8 inches so. length is 8.66 in