Question #150225
8. A right circular cylinder with an altitude of 40 cm and base diameter of 30cm has a right circular cone at its top with the same base. If the cone is 60cm high, determine its lateral area in cm2.

a) 706.86
b) 2,827.43
c) 2,914.45
d) 3,345.76
1
Expert's answer
2020-12-11T13:13:52-0500

The lateral area of a right circular cone with a slant height ll and base radius rr can be found by the formula


AL=πrlA_L=\pi rl

By the Pythagorean Theorem from the right triangle


l2=r2+h2,l^2=r^2+h^2,

where hh is an altitude of a cone.

Given d=30 cm,h=60 cm.d=30\ cm, h=60\ cm.

Then


r=d2=30 cm2=15 cmr=\dfrac{d}{2}=\dfrac{30\ cm}{2}=15\ cm

l=r2+h2=(15 cm)2+(60 cm)2=1517 cml=\sqrt{r^2+h^2}=\sqrt{(15\ cm)^2+(60\ cm)^2}=15\sqrt{17}\ cm

AL=π(15 cm)(1517 cm)=(22517)π cm2A_L=\pi(15\ cm)(15\sqrt{17}\ cm)=(225\sqrt{17})\pi\ cm^2

2914.45 cm2\approx2914.45\ cm^2

c) 2,914.45



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