Question

volume is the number of cubic units needed to fill a given solid. length: 4 in. volume = length × width × height width: 2 in. volume=(4 in.)×(2 in.)×(3 in.) height: 3 in. volume = 24 cubic inches find the volume of each rectangular solid. 1. a b c v = _ cu. in. v = _ cu. yd. v = _ cu. ft. 2. v = _ cu. yd. v = _ cu. ft. v = _ cu. ft. 3. v = _ cu. in. v = _ cu. yd. v = ___ cu. ft. chapter 8, lesson 7 measurement concepts

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - solid is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Solve for part 1a

For the cube with $l = 2$ in, $w = 2$ in and $h = 2$ in, $V=2\times2\times2 = 8$ cu. in.

Step3: Solve for part 1b

For the rectangular - solid with $l = 8$ yd, $w = 3$ yd and $h = 2$ yd, $V = 8\times3\times2=48$ cu. yd.

Step4: Solve for part 1c

For the rectangular - solid with $l = 3$ ft, $w = 1$ ft and $h = 5$ ft, $V=3\times1\times5 = 15$ cu. ft.

Step5: Solve for part 2a

For the rectangular - solid with $l = 4$ yd, $w = 3$ yd and $h = 3$ yd, $V = 4\times3\times3=36$ cu. yd.

Step6: Solve for part 2b

For the rectangular - solid with $l = 9$ ft, $w = 2$ ft and $h = 7$ ft, $V=9\times2\times7 = 126$ cu. ft.

Step7: Solve for part 2c

For the rectangular - solid with $l = 6$ ft, $w = 5$ ft and $h = 3$ ft, $V=6\times5\times3=90$ cu. ft.

Step8: Solve for part 3a

For the rectangular - solid with $l = 7$ in, $w = 2$ in and $h = 8$ in, $V=7\times2\times8 = 112$ cu. in.

Step9: Solve for part 3b

For the rectangular - solid with $l = 5$ yd, $w = 4$ yd and $h = 3$ yd, $V=5\times4\times3 = 60$ cu. yd.

Step10: Solve for part 3c

For the rectangular - solid with $l = 7$ ft, $w = 3$ ft and $h = 9$ ft, $V=7\times3\times9=189$ cu. ft.

Answer:

1a. 8 cu. in.
1b. 48 cu. yd.
1c. 15 cu. ft.
2a. 36 cu. yd.
2b. 126 cu. ft.
2c. 90 cu. ft.
3a. 112 cu. in.
3b. 60 cu. yd.
3c. 189 cu. ft.