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3 years ago

The altitude of the base of a cloud

Mathematics

1 answer:

natima [27]3 years ago

7 0

The height of the ceiling is 162.31 meters

The situation will form a right angle triangle.

<h3>Right angle triangle:</h3>

Right triangle has one of its angles as 90 degree. Therefore, the sides can be found using trigonometric ratios

The triangle formed, the theodolite distance from the spotlight is the adjacent side. Therefore,

tan 62.7 = opposite / adjacent

tan 62.7 = x / 83

cross multiply

x = 83 × tan 62.7

x = 160.809554025 m

Therefore, the height of the ceiling form the ground is as follows:

160.809554025 + 1.5 = 162.309554025 m

learn more on right angle triangle here; brainly.com/question/13481976

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4 years ago

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irakobra [83]

Answer:

V = 240π cm^3 , S= 168π cm^2

Step-by-step explanation:

The given figure is a combination of hemi-sphere and a cone

<u>Volume:</u>

For volume

r = 6 cm

h = 8 cm

$Volume\ of\ cone = \frac{1}{3}\pi r^2h\\= \frac{1}{3}\pi (6)^2*8\\=\frac{1}{3}\pi *36*8\\=\frac{288}{3}\pi\\=96\pi cm^3 \\\\Volume\ of\ hemisphere = \frac{2}{3}\pi r^3\\=\frac{2}{3}*\pi * (6)^3\\=\frac{2}{3}*\pi *216\\=\frac{432}{3}\\=144\pi cm^3 \\\\Total\ Volume= Volume\ of\ cone + Volume\ of\ hemisphere\\= 96\pi +144\pi \\=240\pi cm^3$

<u>Surface Area:</u>

For this particular figure we have to consider the lateral area of the cone shape and surface area of the hemisphere

We have to find the lateral height

$l = \sqrt{r^2+h^2}\\ l = \sqrt{(6)^2+(8)^2} \\l= \sqrt{36+64}\\ l = \sqrt{100}\\l = 10cm\\\\Surface\ area\ of\ cone = \pi rl\\= \pi (6)(10)\\=\pi *60\\=60 \pi\ cm^2\\\\Surface\ area\ of\ hemisphere = 2\pi r^2\\= 2 \pi * (6)\\= 2 \pi *36\\= 72 \pi\ cm^2\\\\Total\ surface\ Area = Surface\ area\ of\ cone + Surface\ area\ of \ hemisphere\\= 60 \pi + 72 \pi\\=132 \pi\ cm^2$

Hence the first option is correct ..

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