A rectangular prism has a volume of 960cm. It's width, length, and height are in the ratio 3:5:8.

A) Determine the dimensions of the prism

B) What is the ratio of the left side to the front to the top of the prism by surface area?

C) Calculate the surface area of the prism.

3x*5x*8x=960

x^3=960/120

x= cubrt(8)=2

sides then are 6;10;16

how do i solve B) though?

this is pif im ov cuz

3x*5x*8x=960

x^3=960/120

x= cubrt(8)=2

sides then are 6;10;1

A) To determine the dimensions of the rectangular prism, let's assign variables to the width, length, and height. Let's say the width is 3x, the length is 5x, and the height is 8x.

Given the volume of the prism is 960 cm³, we can set up the equation:

Volume = width * length * height
960 = (3x) * (5x) * (8x)

To solve for x, we divide both sides of the equation by 120:
960 / 120 = (3x * 5x * 8x) / 120
8 = x³
x = ∛8
x = 2

Therefore, the dimensions of the prism are:
Width = 3x = 3 * 2 = 6 cm
Length = 5x = 5 * 2 = 10 cm
Height = 8x = 8 * 2 = 16 cm

So, the dimensions of the prism are 6 cm (width) x 10 cm (length) x 16 cm (height).

B) To find the ratio of the left side to the front to the top of the prism by surface area, we need to calculate the surface areas of each face.

The surface area of the left side (width x height) is 6 cm x 16 cm = 96 cm²
The surface area of the front (length x height) is 10 cm x 16 cm = 160 cm²
The surface area of the top (width x length) is 6 cm x 10 cm = 60 cm²

The ratio of the left side to the front to the top is therefore 96 cm² : 160 cm² : 60 cm², which can simplified to 3 : 5 : 2.

C) To calculate the surface area of the prism, we need to find the areas of all six faces and add them together.

The area of the left and right sides (width x height) is 2 * (6 cm x 16 cm) = 192 cm²
The area of the front and back sides (length x height) is 2 * (10 cm x 16 cm) = 320 cm²
The area of the top and bottom sides (width x length) is 2 * (6 cm x 10 cm) = 120 cm²

Adding up all the areas, we get:

192 cm² + 320 cm² + 120 cm² = 632 cm²

Therefore, the surface area of the prism is 632 cm².

960/120=8

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