To calculate the surface area, all the values should be in the same unit.
B
b
To find the height of the sand, you should multiply 34 by the height of the sandbox.
A
a
64/3ft^2
B
b
6 ft^3
Practice makes perfect
a
Assuming the sandbox has a bottom, it has 5 surfaces.
Notice that there are two pairs of faces that have the same area. Thereby, the surface of the whole sandbox can be calculated by adding the area of the yellow faces Y twice, the area of the orange faces O twice, and the area of the base B.
S=2Y+2O+B
Let's find all these values and then substitute them into the formula to calculate the surface area.
Yellow Face Area
The yellow faces are rectangles, so to calculate the area we can multiply the width d by the length l.
Y=wl
In this case, the length is 3 feet and the width is 8 inches. We can multiply the values only when they are measured in the same unit. Thus, let's convert the inches into feet using the fact that one foot equals 12 inches.
1foot/12inches
By multiplying the conversion factor by our measurement, we can convert inches into feet.
Similarly, we can calculate the area of the orange faces. The length of the orange face is 4 ft and the width is the same as before, 8 inches or 23 feet. Once more, multiplying the length by the width, we can find the area of the orange face.
We are told that the base is a rectangle with the width of 3 ft and the length of 4 ft. Again, multiplying these values, we can find the area of the base.
B=3* 4=12ft^2
Thus, the base of the prism has the area of 12ft^2.
Total Surface Area
Now, we know the surface area of all the faces.
Y= 2ft^2
O= 83ft^2
B= 12ft^2
Let's substitute these values into the formula for the total surface area that we wrote before and simplify.
Let's assume that the surface of the sand in the sandbox is flat. In this case, the sand itself is also a rectangular prism. Therefore, we can use the formula for the volume of a rectangular prism.
V=Bh
In this formula, B is the area of the base and h is the height of the prism. Let's find B and h. Then we will substitute these values into the formula and calculate the volume of the sand.
Base Area
The base of the sand prism is the same as the bottom of the sandbox. Earlier, we already calculated that the area of the prism's base is 12ft^2.
Height
The height of the sandbox is 8 inches, or 23 feet. It is given that the height of the sand is 34 of the height of the box. Thereby, to calculate the height of the sand, we can multiply 23 by 34.
