Problem 5
Answer: 480 square cm
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Work Shown:
The lateral faces of this pyramid are triangles. Focus on half of one of the triangles. We have a right triangle with a leg of 8 cm and a hypotenuse of 17 cm. The dashed line is the other leg, which we'll find using the pythagorean theorem
a^2 + b^2 = c^2
8^2 + b^2 = 17^2
64 + b^2 = 289
b^2 = 289 - 64
b^2 = 225
b = sqrt(225)
b = 15
Each triangle face has a base of 2*8 = 16 and a height of 15. So the area of one triangle is A = b*h/2 = 16*15/2 = 240/2 = 120
There are four of these triangles, so 4*120 = 480 is the lateral surface area. Basically the surface area for everything but the base.
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Problem 6
Answer: 137.4 square cm
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Work Shown:
L = slant height = 12.5
h = height of cone = 12
To find the radius, we form a right triangle such that the height 12 is one leg and the hypotenuse is 12.5; the unknown radius is the other leg of this right triangle.
So,
a^2 + b^2 = c^2
(12)^2 + b^2 = (12.5)^2
144 + b^2 = 156.25
b^2 = 156.25 - 144
b^2 = 12.25
b = sqrt(12.25)
b = 3.5
The radius is therefore 3.5 cm
Now let's use that formula given
LSA = lateral surface area of the cone
LSA = pi*r*L
LSA = pi*3.5*12.5
LSA = pi*43.75
LSA = 43.75pi <<-- exact lateral surface area in terms of pi
LSA = 137.444678594553 <<--- approx lateral surface area
LSA = 137.4 <<--- rounding to nearest tenth (aka 1 decimal place)
