Answer:
4. h=9in
5. 150.8
6. 301.6
Explanation:
4.
Surface area of a rectangular prism form : A=2(wl+hl+hw)
Substitute in values from the question: 558=2[(9)(11)+h(11)+h(9)]
Multiply where applicable: 558=2[(99)+11h+9h]
Combine like terms: 558=2[(99)+20h]
Divide both sides by 2: 279=(99)+20h
*note- This step can also be seen as multiplying the right side by 2 without messing with the left at all (558=(198)+40h) then you would solve in the same fashion as I will from here just with the alternative numbering*
Subtract to isolate the h: 180=20h
Divide both sides to isolate the h: 9=h
Now we see that the missing dimension h=9in
*note- I did not bold the equations with squares so please don't be confused by that*
5.
Surface area of a cylinder form: A=2πrh+2π
Substitute in values from the question: A=2π(3)(5)+2π
Multiply were applicable: A≈94.2+56.5
Add remaining values: A≈150.8
Now we see that the total surface area is 150.8
*note- whenever we solve for volume or SA of a figure we square the unit (
➞
)*
6.
Surface area of a cylinder form: A=2πrh+2π
Substitute in values from the question: A=2π(6)(2)+2π
*note- we use 6 instead of the given value 12 because the equation calls for the radius and not the diameter*
Multiply were applicable: A≈75.2+226.2
Add remaining values: A≈301.6
Now we see that the total surface area is 301.6
*note- whenever we solve for volume or SA of a figure we square the unit (
➞
)*
Hope this helps :)