Question #149024
1. Determine the lateral area of a cylinder of height 300mm and base radius of 100mm.

2. 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.
1
Expert's answer
2020-12-15T07:16:28-0500

h=300  mmr=100  mmLateral  area  of  cylinder=2πrh=2×3.14×100×300=188520  mm2h = 300\; mm \\ r = 100 \;mm \\ Lateral \;area\; of \;cylinder = 2πrh \\ = 2 \times 3.14 \times 100 \times 300 \\ = 188520 \; mm^2

Answer: 188520 mm2

The lateral surface area S1S_1 of a right circular cylinder with an altitude of h1=40 cmh_1=40\ cm and base diameter of d=30 cmd=30\ cm is equal to S1=πdh=π4030=1200πS_1=\pi \cdot d\cdot h=\pi\cdot 40\cdot 30=1200\pi (cm2cm^2 )

The lateral surface area S2S_2 of a right circular cone with an altitude of h2=60 cmh_2=60\ cm and base diameter of d=30 cmd=30\ cm is equal to S2=πrlS_2=\pi \cdot r\cdot l, where r=d2=15 (cm)r=\frac{d}{2}=15\ (cm) is the radius of the base and l=(h2)2+r2=602+152=3600+225=3825=1517 (cm)l=\sqrt{(h_2)^2+r^2}=\sqrt{60^2+15^2}=\sqrt{3600+225}=\sqrt{3825}=15\sqrt{17}\ (cm) is the slant height of the cone Therefore, S2=π151517=22517π (cm2)S_2=\pi\cdot 15\cdot 15\sqrt{17}=225\sqrt{17}\pi\ (cm^2).

The lateral surface area of a right circular cylinder with a right circular cone at its top is1200π+22517π=75π(16+317) (cm2).1200\pi+225\sqrt{17}\pi=75\pi(16+3\sqrt{17})\ (cm^2).



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