Question

HELP! Two right rectangular prisms are shown below. If each prism is packed with small cubes of side length 1/4 inch how many more cubes are in prism 2

A. 42 Cubes B. 48 Cubes

C. 510 Cubes D. 720 Cubes

Answer 1

First find the volume of the two rectangular prisms using the formula:

V = l · w · h

Where 'l' represents the length, 'w' the width, and 'h' the height.

Now let's find the volume of Prism 1;

V = l · w · h

V = 7/4 · 3/2 · 5/4

V = (7/4 · 3/2) · 5/4

V = 21/8 · 5/4

V = 105/32 cubic inches.

Now let's find the volume of Prism 2;

V = l · w · h

V = 5/2 · 9/4 · 2

V = (5/2 · 9/4) · 2

V = 45/8 · 2/1(make 2 to 2/1 because it makes it a bit easier)

V = 90/8 cubic inches.

Now let's find how many cubes can fit into each of these prisms.

But first, we need to find out the volume of one cube.

• Remember, all sides to a cube are equal.

Using the formula, V = l · w · h;

1/4 · 1/4 · 1/4

= 1/64 cubic inches is the volume of one cube.

Now we find how many cubes can fit inside each of these prisms.

Prism 1:

105/32(volume for this prism) ÷ 1/64(volume of one cube)

= 210 cubes can fit inside prism one.

Prism 2:

90/8(volume for this prism) ÷ 1/64(volume of one cube)

= 720 cubes can fit inside prism two.

Finally, let's calculate their difference:-

720 - 210

= 510 cubes.

Hence, prism 2 can hold 510 more cubes than prism 1.