A rectangular prism has a width of 92 ft and a volume of 240 ft3 find the volume of a similar prism with a width of 46 ft round to the nearest tenth if necessary

Question

1. 30 ft3
2. 40 ft3
3. 60 ft3
4. 120 ft3

Answer 1

4. 120 ft3

Explanation:

Since the two prisms are similar, their corresponding dimensions are proportional.

Let the length, height, and length of the second prism be x, y, and z respectively.

Then, we have:

x : 46 = y : y/2 = z : 92

Simplifying each ratio, we get:

x : 46 = y : 2y = z : 92

From the given information, we know that the volume of the first prism is 240 ft3.

Volume of first prism = width x height x length

240 = 92 x y x z

Solving for y and z, we get:

y = 240/(92 x z)

z = 240/(92 x y)

Substituting these values into the ratio equation, we get:

x : 46 = (240/(92 x z)) : (480/(92 x z)) = (240/(92 x y)) : (92/(92 x y))

Simplifying, we get:

x : 46 = 5 : 10

Therefore, x = 23.

Now we can find the volume of the second prism:

Volume of second prism = width x height x length

= 46 x (2y) x 23

= 92y x 23

Substituting y = 240/(92 x z) and z = 240/(92 x y) into the formula, we get:

Volume of second prism = 240 x 23

= 5520

Rounding to the nearest tenth, we get 5520.0, which is approximately 120 ft3.