Lydia Rise us building a terraium and needs to buy two sizes of gravel and soil to go in the bottom. The terraiun is 24 in longs, 14 in wide, and 15 in tall.
A.The bottom layer is pea gravel and needs to be 2 inches deep. How many cubic inches will she need? B. The second layer is aquarium gravel and needs to be 1 inch deep. She has 400 cubic inches of gravel, does she have enough?C.The top layer is potting soil. It needs to be 5 in deep. The ptting soil comes in bags of 1,500 cubic inches. How many bags will she need?
How have you started these problems?
Where did you get stuck?
this whole thing makes no sense to me. can you please answer it?
The major part of this problem involves volume.
The volume of a rectangular prism is:
V = l * w * h
Since the bottom layer is 2 inches deep --
V = 24 * 14 * 2
V = 672 cubic inches
Now figure out the volume of each of the other two layers.
A. To calculate the number of cubic inches of pea gravel needed for the bottom layer, you need to find the surface area of the terrarium's base and multiply it by the desired depth.
The formula for surface area is: length * width.
Given that the dimensions of the terrarium are: length = 24 inches and width = 14 inches, the surface area is: 24 * 14 = 336 square inches.
Multiplying the surface area by the desired depth of 2 inches, we get: 336 * 2 = 672 cubic inches of pea gravel needed for the bottom layer.
Therefore, Lydia would need 672 cubic inches of pea gravel for the bottom layer.
B. To determine if Lydia has enough aquarium gravel for the second layer, we subtract the volume of the pea gravel layer from the total volume of aquarium gravel she has.
Given that Lydia has 400 cubic inches of aquarium gravel, we need to subtract the volume of pea gravel (672 cubic inches) from it: 400 - 672 = -272.
Since the result is negative (-272), this means Lydia does not have enough aquarium gravel to fulfill the 1-inch depth requirement for the second layer.
C. To calculate the number of bags of potting soil Lydia needs for the top layer, we first need to find the volume of potting soil required.
Using the formula for volume: length * width * depth, and given that the length is 24 inches, the width is 14 inches, and the desired depth is 5 inches, we can calculate the volume: 24 * 14 * 5 = 1,680 cubic inches.
Since the bags of potting soil are sold in sizes of 1,500 cubic inches each, we divide the required volume by the bag size to find how many bags are needed: 1,680 / 1,500 = 1.12 bags.
However, since you cannot purchase a fraction of a bag, Lydia would need to round up to the nearest whole number. Therefore, she would need to buy 2 bags of potting soil for the top layer.
To summarize:
A. Lydia needs 672 cubic inches of pea gravel for the bottom layer.
B. No, Lydia does not have enough aquarium gravel for the second layer.
C. Lydia needs 2 bags of potting soil for the top layer.