Question

A rectangular planter that is 4 feet long, 4 feet wide, and 2 feet deep uses three bags of potting soil. The amount of potting soil needed depends on the volume of the planter. How many bags of soil would be used in a planter that had a base area of 40 square feet and a depth of 4 feet? Fill in the blanks to complete the explanation. The first planter has a volume of ______ cubic feet and uses 3 bags of potting soil. The second planter has a volume of _____ cubic feet. The volume of the second planter is _____ times ad much as the volume of the first planter. Multiply the 3 bags of potting soil used in the first planter by_____ to find that_____ bags of potting soil would be used in the second planter.

Answer 1

The answers to the five blanks are as follows;

1. 32,

2. 160,

3. 5,

4. 5, and

5. 15.

Explanation:

Step 1; The volume of a rectangular box is given by multiplying the length, width and height of the box.

The volume of the first planter = length × width × height.

Length = 4 feet, Width = 4 feet and height = 2 feet.

The volume of the first planter = 4 × 4 × 2 = 32 cubic feet. This is the answer to the first blank.

Step 2; The volume can also be calculated by multiplying the area of the rectangle by its height.

The volume of the second planter = Area × height = 40 × 4 = 160 cubic feet. This is the answer to the second blank.

Step 3;
`(thevolumeofthesecondplanter)/(thevolumeofthefirst planter)` =
`(160)/(32)` = 5. So the second planter is 5 times bigger than the first planter. This is the answer to the third blank.

Step 4; So if the first planter needs 3 bags of soil, the second planter will need 5 times more than the first planter. This is the answer to the fourth blank.

So if the first planter needs 3 bags and the second planter is five times bigger it needs = 3 × 5 = 15 bags of potting soil. This is the answer to the fifth blank.