A cone has a height of 24 cm and its base has a radius of 15 cm. If the cone is horizontally cut into two segments 12 cm from the base, what would the surface area of the bottom segment be?

2 Answers

22.1 SQ CM

Explanation:

Requires reworking based on the details given below

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A_T= A_B + A_b + L_R - L_r

Where A_T is Total Surface Area of the bottom truncated cone, A_B is the area of the bottom circular base, A_b is the area of the circular base of top cut cone, L_R is the Lateral Surface Area of the whole cone and l_r is the Lateral Surface Area of the top half cone.

Feb 23, 2018

Total Surface Area of the bottom segment of the cone

A_(R-r) = color(purple)(1882.6)cm^3

Explanation:

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r / R = h / H

r = (15 * (24-12))/24 = 7.5 cm

Lateral surface are of a cone L_R= pi R L

Now we have to find L

L = sqrt(R^2 + H^2) = sqrt(15^2 + 24^2) ~~ 28.3 cm

L_R = pi * 15 * 28.3 ~~ 1333.6 cm^2

Similarly,l = sqrt(12^2 + 7.5^2) ~~ 14.2 cm

l_r = pi r l = pi * 7.5 * 14.2 ~~ 334.6

Area of base of a cylinder A_R = pi R^2 = pi * 15^2 ~~ 706.9

Similarly, A_r = pi r^2 = pi * 7.5^2 ~~ 176.7

Total surface area of the truncated cone

A_(R-r) = L_R - l_r + A_R + A_r = 1333.6 - 334.6 + 706.9 + 176.7 = color(purple)(1882.6)cm^3