Ali measures the rectangular area of his driveway he wants to fill with gravel to be 4 yards by 50 yards. He orders 80 cubic yards of gravel.
a) How deep will the layer of gravel be on the driveway
b) If Ali had ordered 20 cubic yards more gravel , how much deeper would gravel be?
I’m not sure how to do this please help thank you.
length * width = area
length * width * height = volume
That means that area * height = volume
here
area = 50 * 4 = 200 square yards
height = volume / area = 80/200 = 0.40 yards (which is about 14 1/2 inches)
If he used 100 cubic yards then
new height =100/200 = 0.50 yards which is 1/10 yard deeper (around 4 inches deeper for total depth of .5*36 = 18 inches)
Thank you so much anonymous for your help with my math question . I really appreciate it .
To find the depth of the layer of gravel on the driveway, you need to divide the total volume of gravel by the area of the driveway. Here's how you can find the solution step by step:
a) How deep will the layer of gravel be on the driveway?
Step 1: Calculate the area of the driveway.
The formula to calculate the area of a rectangle is length multiplied by width. In this case, the length is given as 4 yards, and the width is given as 50 yards. So the area would be:
Area = Length * Width
Area = 4 yards * 50 yards
Area = 200 square yards
Step 2: Calculate the depth of the layer of gravel.
Since the volume of gravel is given as 80 cubic yards, and the area of the driveway is 200 square yards, you can divide the volume by the area to find the depth:
Depth = Volume / Area
Depth = 80 cubic yards / 200 square yards
Depth = 0.4 yards
So the layer of gravel on the driveway will be 0.4 yards (or 14.4 inches) deep.
b) If Ali had ordered 20 cubic yards more gravel, how much deeper would the gravel be?
To find out how much deeper the gravel would be, you can use the same formula again:
New Depth = (Volume + Additional Volume) / Area
Step 1: Calculate the new volume of gravel.
Since Ali ordered 20 cubic yards more gravel, you can add this to the original volume:
New Volume = Volume + Additional Volume
New Volume = 80 cubic yards + 20 cubic yards
New Volume = 100 cubic yards
Step 2: Calculate the new depth of the layer of gravel.
Now, you can substitute the new volume into the formula and find the new depth:
New Depth = New Volume / Area
New Depth = 100 cubic yards / 200 square yards
New Depth = 0.5 yards
Therefore, if Ali had ordered 20 cubic yards more gravel, the layer of gravel would be 0.5 yards (or 18 inches) deep.