Question

Comparing Rectangular Solids

One rectangular solid with a square base has twice the height of another rectangular solid with a square base with

the same side length. Which statements about the two rectangular solids are true? Check all that apply.

The bases are congruent.

The solids are similar.

The ratio of the volumes of the first solid to the second solid is 8:1.

The volume of the first solid is twice as much as the volume of the second solid.

If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second

solid.

Done

C00Dannnnnn

Answer 1

A, D ,E

Explanation:

Answer 2

The bases are congruent.

The volume of the first solid is twice as much as the volume of the second solid.

If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.

Explanation:

From the above answers; the term congruent means two similar objects or shapes having the same pattern or structure. From the question; we are being told that the two rectangular solid have a square base hence; they are both congruent in nature .

Also;

The volume of the first solid is twice as much as the second solid . i.e 2:1

If the volume of the first solid is :
`x*x*2 \ h` =
`2x^2 \ h`

Then the volume of the second solid is =
`x*x*h = x^2h`

thus ; they are in the ratio of 2:1

FInally: If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second

The surface area of the first solid is :

`=2[x*x+(2 H*x+2 H*x)] \\ \\ =2[x^2+4 Hx] \\ \\ = 2x[x + 4Hx]`

Then the second solid is :

`2[x*x+x* H+ H*x] \\ \\ =2[x^2+2 Hx] \\ \\ =2x[x+ 2H]`

Therefore:

`S_1 = S_2 + 4Hx`