Find the measure of the angle formed between the base of the cone and a line segment that represents the slant height

Mathematics

1 answer:

wel3 years ago

6 0

Since there are no figures given, I will give an example.

You are given a silo that is shaped as a closed cylinder with a conical end. The diameter of the silo is 4 ft, the length of the cylindrical part is 6 ft, and the entire length of the silo is 10.5 ft. Suppose that you are asked to find the total volume of grains that can be stored in the silo.

Given:

Cylinder part

D = 4 ft

H = 6 ft

Cone part

H = 10.5 – 6 = 4.5ft

D = 4ft

Required:

Volume of silo

Solution:
V of cylinder = πr²H

V of cylinder = π(4/2)²(6)

V of cylinder = 75.4 ft³

V of cone = πr²H/3

V of cone = π(4/2)²(4.5/3)

V of cone = 18.85 ft³

Total volume = 94.25 ft³

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6 0

3 years ago

Cot y, if csc y =-10/3 and cos y< 0

fredd [130]

$\csc y=-\dfrac{10}3\implies\sin y=-\dfrac3{10}$

$\cos^2y=1-\sin^2y\implies \cos y=\pm\sqrt{1-\dfrac9{100}}=\pm\dfrac{\sqrt{91}}{10}$

You're told that $\cos y$ , so omit the positive root.

$\cot y=\dfrac{\cos y}{\sin y}=\dfrac{-\frac{\sqrt{91}}{10}}{-\frac3{10}}=\dfrac{\sqrt{91}}3$