Answer: 320ft², ~326.73cm², ~628.32mm², 186yd², ~615.75m², 96in²,
2376ft³
Explanation:
8) For a cube we will find the area of the three pairs of squares
First pair: 8ft * 6ft = 48ft² Second pair: 8ft * 8ft = 64ft²
Third pair: 8ft * 6ft = 48ft² (I think that says 6? Could say 5)
Multiply each pair by two and add them up:
48ft² * 2 = 96ft² 64ft² * 2 = 128ft² 48ft² * 2 = 96ft²
96ft² + 128ft² + 96ft² = 320ft²
9) For a cylinder we will add the area of the lateral area and the two circles
Lateral Area: 8πcm * 9cm = 72πcm² or ~226.19cm²
Area of one circle: π*4² = 16π or ~50.27cm²
Multiply that by 2 and we get ~100.54cm²
Then we add up 100.54cm² and 226.19cm² to get the answer: ~326.73cm²
10) For the cone we will use: A = πr(r + √(h² + r²))
A = 8πmm(8mm + √(15²mm + 8²mm))
A = 8πmm(8mm + 17mm)
A = 8πmm*25mm = ~628.32mm²
11) I will start with the two triangles
One triangle: 1/2 * 6yd * 8yd = 24yd²
Two triangles = 48yd²
Next, the two rectangles in the back
Base rectangle: 8yd * 5yd = 40yd²
Back Triangle: 6yd * 8yd = 48yd²
Lastly, the top triangle
Top Triangle: 10yd * 5yd = 50yd²
Add them up to get: 186yd²
12) For a sphere I will use: A = 4πr²
A = 4π(7m)²
A = 4π * 49m²
A = 196πm² OR ~615.75m²
13) For a pyramid I will use: A = a² + 2a√((a²/4)+h²)
A =(6in)² + 2*(6in)*√((6²/4)+4²)
A = 36in² + 12in*√(9²+16in²)
A = 36in² + 12in * 5in
A = 36in² + 60in² = 96in²
Extra Credit!
14) What is the volume of a pool with dimensions: 22ft long, 18ft wide, and 6 ft deep?
Strangely, the Extra Credit is much easier than the original problems but I'm not complaining!
Simply multiply each dimension and you get the volume of the pool, so:
22ft * 18ft * 6ft = 2376ft³
I hope this helped!