1.What is the area of a rectangular cardboard if its length and base are 3√12 cm and 2√3 cm respectively?
2.Find the value of the variable that will make the equation 10 + √(10m-1) = 13 true.
Answers
Answer:
Finding the Volume and Surface Area of Rectangular Solids
LEARNING OUTCOMES
Find the volume and surface area of a rectangular solid
A cheerleading coach is having the squad paint wooden crates with the school colors to stand on at the games. (See the image below). The amount of paint needed to cover the outside of each box is the surface area, a square measure of the total area of all the sides. The amount of space inside the crate is the volume, a cubic measure.
This wooden crate is in the shape of a rectangular solid.

Each crate is in the shape of a rectangular solid. Its dimensions are the length, width, and height. The rectangular solid shown in the image below has length 44 units, width 22 units, and height 33 units. Can you tell how many cubic units there are altogether? Let’s look layer by layer
a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This 44 by 22 by 33 rectangular solid has 2424 cubic units.

Altogether there are 2424 cubic units. Notice that 2424 is the length×width×height.length×width×height.
The volume, VV, of any rectangular solid is the product of the length, width, and height.
V=LWHV=LWH
We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, BB, is equal to length×width.length×width.
B=L⋅WB=L⋅W
We can substitute BB for L⋅WL⋅W in the volume formula to get another form of the volume formula.

We now have another version of the volume formula for rectangular solids. Let’s see how this works with the 4×2×34×2×3 rectangular solid we started with. See the image below.

To find the surface area of a rectangular solid, think about finding the area of each of its faces. How many faces does the rectangular solid above have? You can see three of them.
Afront=L×WAside=L×WAtop=L×WAfront=4⋅3Aside=2⋅3Atop=4⋅2Afront=12Aside=6Atop=8Afront=L×WAside=L×WAtop=L×WAfront=4⋅3Aside=2⋅3Atop=4⋅2Afront=12Aside=6Atop=8
Notice for each of the three faces you see, there is an identical opposite face that does not show.