I NEED YOUR HELP ASAP!!! GRADE 11 APPLIED WORD PROBLEM.

Question

A pet store designs fish tanks that are in the shape of a rectangular prism. The small tank has a capacity of 1920 cu in. The scale factor that relates the dimensions of the small tank to the dimensions of the medium tank are 1.25. The scale factor that relates the dimensions of the medium tank to the dimensions of the large tank are 1.2.

Glass costs the store $12 to put in the small tank.

Find the capacity of the medium and large tanks and find the cost of the glass for the medium and large tanks.

please show all work.

Answer 1

S:M:L = 1:1.25:1.2 for dimensions

1920 in^3 is capacity of the small tank

let the small rectangular prism be 20 by 8 by 12

then medium prism is 25 by 10 by 15

and the large is 30 by 12 by 18

the small capacity = 20x8x12 = 1920

the medium = 25x10x15 = 3750 in^3

the large =30x12x18 = 6480 in^3

1920:3750:6480 3= ratio of volumes for Small:Medium:Large

glass on 6 sides

for small the surface area is 2(20x8 + 8x12 + 20x12) = 2(160+96+240) = 2(496) = 992 in^2

for the medium

2(25x10 + 25x15+ 10x15) = 2(250+375+150)=2(775) = 1450 in^2

for the large

2(30x12 + 30x18 + 12x18) = 2(360+ 540 + 216) = 2(1116) = 2232 in^2

$12 for 992,

1450 x 12/992 = about $17.54

for the large

2232 x 12/992 = $27