A rectangular solid has a top face with surface area of 28 ft, a front face with surface area of 20 ft, and a side face with surface area of 70 ft. What is the volume of this solid?

There are two ways to approach the problem:

1. Calculate the side lengths, a,b and c.
ab=28....(1)
ac=20....(2)
bc=70....(3)

Therefore by dividing ac by bc, we get
a/b=2/7
substitute a=2b/7 into equation (1) gives 2b/7*b=28 => b²=98 => 7√2

You can calculate similarly the other sides.

2.
You are looking for the product abc, from which ab=28
So
abc=ab*bc*√((a/b)/ab)
All the products are known, the quotient has been calculated in part 1.
So the volume abc can be calculated directly.

umm still lost.....

Did you try method 1 or method 2?

To find the volume of a rectangular solid, we need to know the dimensions of the solid. Let's assume the length (L), width (W), and height (H) of the solid.

We are given three surface areas - the top face (A_top = 28 ft^2), the front face (A_front = 20 ft^2), and the side face (A_side = 70 ft^2).

The surface area of each face of a rectangular solid can be calculated as follows:

Top face: A_top = L × W
Front face: A_front = L × H
Side face: A_side = W × H

We can use these equations to solve for the dimensions of the solid.

From the given information, we have the following system of equations:

A_top = L × W = 28 ft^2
A_front = L × H = 20 ft^2
A_side = W × H = 70 ft^2

To solve this system of equations, we can use substitution or elimination method, or even solve it graphically. Let's use the substitution method:

Since we have an equation for A_top in terms of L and W, we can solve for one variable in terms of the other:

L = 28 ft^2 / W

Now substitute this value of L into the equation for A_front:

(28 ft^2 / W) * H = 20 ft^2

Simplify:

28H = 20W

Now substitute this value of H into the equation for A_side:

W * (20W/28) = 70 ft^2

Simplify:

10W^2 / 14 = 70

Simplify further:

5W^2 / 7 = 70

Multiply both sides by 7:

5W^2 = 490

Divide both sides by 5:

W^2 = 98

Taking the square root of both sides:

W = √98 ≈ 9.899 ft

Now substitute this value of W back into the equation for L:

L = 28 ft^2 / W ≈ 28 ft^2 / 9.899 ft ≈ 2.828 ft

Now that we have the dimensions of the rectangular solid (L ≈ 2.828 ft, W ≈ 9.899 ft, H is yet to be determined), we can calculate its volume using the formula:

Volume = Length × Width × Height

Volume = 2.828 ft × 9.899 ft × H

The volume of the solid depends on the height (H). Unfortunately, the given information does not provide us with the value of the height. Therefore, the volume of this solid cannot be determined without additional information.