If the edges of the base of a rectangular prism are 8cm and 6cm, and the diagonal is 10--square root of 2, what is the volume of the solid?

diagonal of rectangular base = sqrt(8^2+6^2) = sqrt 100 = 10

so if height is h
h^2 + 10^2 = (10 sqrt 2)^2 = 200
h^2 = 200 - 100 = 100
h = 10
6*8*10 = ?

To find the volume of a rectangular prism, we need to know the length, width, and height. In this case, we are given the lengths of two edges of the base and the length of the diagonal.

Let's first find the height or the third edge of the rectangular prism. Since we know the lengths of two edges of the base (8 cm and 6 cm) and the length of the diagonal, we can use the Pythagorean theorem to find the height.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the base is the hypotenuse, and the lengths of the edges are the other two sides of the right triangle. Therefore, we have:

(8 cm)^2 + (6 cm)^2 = (height)^2

Simplifying this equation:

64 cm^2 + 36 cm^2 = (height)^2
100 cm^2 = (height)^2

Now, we take the square root of both sides to find the height:

√(100 cm^2) = √((height)^2)
10 cm = height

Now that we know the height of the rectangular prism is 10 cm, we can calculate the volume by multiplying the lengths of all three edges:

Volume = length × width × height
Volume = 8 cm × 6 cm × 10 cm
Volume = 480 cm^3

Therefore, the volume of the solid is 480 cubic centimeters.