Find the volume of a right circular cone that has a height of 5.7 m and a base with a circumference of 2.3 m. Round your answer to the nearest tenth of a cubic meter.

Volume of the cone is approximately 0.8 cubic meters

Step-by-step explanation:

Recall that the volume of a circular cone is defined by:

where R is the radius of the cone's base, and H the cone's height. Since we have the information of the height H (5.7 m) we just need to find the radius R. We can do such by using the other piece of information: the circumference of its base.

The circumference of a circle is the product:

So by knowing the circumference's length (2.3 m)  we can solve for the radius R:

We can now use this result in the formula for the volume:

which can be rounded to the nearest tenth as:

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9