Question

A rectangular prism has sides that are in the ratio of 3:5:9. If the volume of the prism is 8640 cm3, then the surface area of the prism, in square millimetres, is_______?

Answer 1

The surface area of the rectangular prism is 278400 square millimeters, if a rectangular prism has sides that are in the ratio of 3:5:9 and the volume of the prism is 8640 cubic centimeters.

Explanation:

The given is,

Volume of Rectangular prism - 8640 Cubic centimeters

Ratio of rectangular prism sides are 3:5:9

Step:1

Formula for volume of rectangular prism,

`Volume, V = whl`...................................(1)

Where, w - width of the prism

h - Height of the prism

l - Length of the prism

Let, x - side of the rectangular prism

From given values,

Volume, V = 8640 cubic centimeters

Width, w =
`(3)/(17)x`

Height, h =
`(5)/(17) x`

Length, l =
`(9)/(17)x`

Equation (1) becomes,

`8640=((3)/(17)x)((5)/(17) x)((9)/(17)x)`

`= 0.027478 x^(3)`

`x^(3)= (8640)/(0.027478)`

`x = \sqrt[3]{314432}`

`= 68`

Step:2

Width, w =
`(3)/(17)x`
`= ((3)/(17)) (68)`
`= 12 cm`

Height, h
`= ((5)/(17) )(68) = 20 cm`

Length, l
`= ((9)/(17))(68)=36cm`

Step:3

Formula for surface area of rectangular prim,

`A= 2(wl+lh+hlw)`

From the values of w, l and h,

`= 2 [(12)(20)+(36)(20)+(36)(12)]`

`= 2 (240+720+432)`

`= 2(1392)`

= 2784 Square centimeters

= 2784 × 100 square millimeters

( 1 square centimeters = 100 square millimeters )

A = 278400 square millimeters

Result:

The surface area of the rectangular prism is 278400 square millimeters, if a rectangular prism has sides that are in the ratio of 3:5:9 and the volume of the prism is 8640 cubic centimeters.