Question

calculate the surface area and volume of a right cone with a slant height of 2 feet and a base circumference of 10(pie) feet.

Answer 1

calculate the surface area and volume of a right cone with a slant height of 2 feet and a base circumference of 10(pie) feet.

According to task:

$l = 2$ feet

Solution:

Find surface area:

So the surface area of the cone equals the area of the circle plus the area of the cone and the final formula is given by:

$$S = \pi r ^ {2} + \pi r l$$

Find r:

Circum $= 2\pi r\rightarrow r = \frac{\text{circum}}{2\pi} = 1.59$

Calculate surface area:

$$S = \pi * 1.59^2 + \pi * 1.59 * 2 = 17.93 \text{feets}^2$$

Find volume:

$$V = \frac {S _ {b} * h}{3}$$

Find $S_{b}$ :

$$S _ {b} = \pi r ^ {2} = 7.94$$

Find h from right triangle:

$$h = \sqrt {l ^ {2} - r ^ {2}} = 1.21$$

Calculate volume:

$$V = \frac {7.94 * 1.21}{3} = 3.2 \text{feets}^3$$