Answer to Question #149313 in Trigonometry for yui

Question #149313
Find the volume and lateral surface area of the frustum of a regular square pyramid whose altitude is 38 cm and whose base edges are 10 cm and 20 cm respectively.

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Expert's answer
2020-12-07T20:27:39-0500

"V = \\frac {1}{3}h(S_1+\\sqrt{S_1S_2}+S_2)"

"\\text{where h is the height of the pyramid;} S_1,S_2\\text{the area of the bases}"

"\\text{since a regular square pyramid:}"

"S_1 = 10*10 =100"

"S_2 = 20*20=400"

"V = \\frac {1}{3}*38*(100+\\sqrt{100*400}+400) \\approx8867\\ cm^3"

"S_{sur}= \\frac{1}{2}(p_1+p_2)*f"

"\\text{where } p_1,p_2 \\text{ the perimeters of the bases } f \\text{ apothem}"

"p_1 = 10 *4 =40"

"p_2 = 20*4=80"

"f = \\sqrt{h^2+{[\\frac{b-a}{2}]}^2}"

"\\text{where }h \\text{ is the height of the pyramid}"

"a,b \\text{ base side length}"

"f = \\sqrt{38^2+{[\\frac{20-10}{2}]}^2}\\approx38.33"

"S_{sur}= \\frac{1}{2}(40+80)*38.33\\approx2299.8\\ cm^2"


Aswer: "V \\approx8867\\ cm^3" "S_{sur}\\approx2299.8\\ cm^2"

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