Question

Find the surface area of each figure to the nearest tenth. Show your work, please

Answer 1

Pyramid surface area (total): Lateral surface area + Base area

Lateral surface area =
`(2p*a)/(2)` where p is the base perimeter and a the apothem.

The base is a sqaure so, find the area of the square.

Base Area = 16*16 = 256 in²

Calculate the perimeter = 16*4 = 64 in

LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²

TSA = 544+256 = 800 in²

Total surface of cone: LSA + Base Area

LSA = πra

Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.

a = √8²+3² = √64+9 = √73 ≈ 8,5 in.

Base area (area of the circle) = πr² = 3²*π = 9π in²

LSA = 3*8,5*π = 25,5π in²

TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²