What is the lateral area, total area, and volume of a rectangular solid whose l=7, w=6, & h=2?
I'm assuming length is depth.
A rectangular solid has 6 sides, so the total area will simply be 6 times the area of one side.
The area of one side is the area of square which is w*h.
The volume of a rectangular solid is l*w*h.
From Google,
"The lateral area is the surface area of a 3D figure, but excluding the area of any bases."
So if you were to take the solid and flatten it, you would get the area of four sides.
Lateral Area = 4*h*w
THANK YOU. THIS REALLY HELPED =]
Whoops, I read those numbers wrong.
The area of two sides will be l*h and the other four will be w*h.
So the total area = 2(l*h) + 4(w*h)
Sorry about that :S
To find the lateral area, total area, and volume of a rectangular solid, you need to use the formulas for each of these measurements. Let's go through each calculation step by step.
1. Lateral Area:
The lateral area refers to the combined area of all the sides of the rectangular solid except the top and bottom faces. To calculate the lateral area, multiply the height (h) by the sum of the lengths of the two sides (l and w), and then multiply the result by 2. The formula for lateral area is: Lateral Area = 2hw + 2lh.
Using the given values:
Lateral Area = 2 × 2(7 + 6)
Lateral Area = 2 × 2(13)
Lateral Area = 2 × 26
Lateral Area = 52 square units
So, the lateral area of the rectangular solid is 52 square units.
2. Total Area:
The total area includes all six faces of the rectangular solid. To find the total area, multiply the length (l) by the width (w), then multiply the width (w) by the height (h), and finally, multiply the height (h) by the length (l). Afterwards, sum up these results. The formula for total area is: Total Area = 2lw + 2wh + 2lh.
Using the given values:
Total Area = 2(7)(6) + 2(6)(2) + 2(2)(7)
Total Area = 84 + 24 + 28
Total Area = 136 square units
So, the total area of the rectangular solid is 136 square units.
3. Volume:
The volume of a rectangular solid is obtained by multiplying the length (l) by the width (w) and then multiplying the result by the height (h). The formula for volume is: Volume = lwh.
Using the given values:
Volume = 7 × 6 × 2
Volume = 84 cubic units
So, the volume of the rectangular solid is 84 cubic units.
To summarize:
- The lateral area is 52 square units.
- The total area is 136 square units.
- The volume is 84 cubic units.