The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume? 500 cm 3 250 cm 3 200 cm 3 150 cm

Question

asked Aug 3, 2020 155k views

2 Answers

Mithson · Answer 1 · 2020-08-07T23:27:37+0000

Answer:

$V=250\ cm^(3)$

Explanation:

step 1

Find the length of the base L

we know that

The surface area of a rectangular prism is equal to

SA=2B+PH

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

substitute

SA=2(LW)+2(L+W)H

we have

$W=5\ cm$

$H=10\ cm$

$SA=250\ cm^(2)$

substitute in the formula and solve for L

250=2(5L)+2(L+5)10

250=10L+20L+100

30L=250-100

$L=5\ cm$

step 2

Find the volume of the rectangular prism

The volume is equal to

V=(LW)H

we have

$W=5\ cm$

$L=5\ cm$

$H=10\ cm$

substitute

$V=(5*5)*10=250\ cm^(3)$