Question

Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 14 cm and its radius is 4.5 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3

Answer 1

Answer:

Surface area = $261.6cm^2$

Volume = $281.2cm^3$

Step-by-step explanation:

To find the surface area of our cone, we are using the formula for the surface area of a cone:

$A=\pir(r+\sqrt{h^2+r^2} )$

where

$A$ is the surface area

$r$ is the radius

$h$ is the height

Notice that the height, radius, and slant height make a right triangle, so to find the height, $h$, we can use the Pythagorean theorem:

$s^2=r^2+h^2$

$14^2=4.5^2+h^2$

$196=20.25+h^2$

$h^2=196-20.25$

$h^2=175.75$

$h=\sqrt{175.75}$

$h=13.26$ cm

We have all we need now to find the surface area of our cone:

$A=\pir(r+\sqrt{h^2+r^2} )$

$A=\pi(4.5)(4.5+\sqrt{13.26^2+4.5^2} )$

$A=261.6cm^2$

Now, to find the volume of our cone, we are using the formula for the volume of a cone:

$V=\frac{\pi r^2h}{3}$

where

$V$ is the volume

$r$ is the radius

$h$ is the height

Replacing values

$V=\frac{\pi (4.5^2)(13.26)}{3}$

$V=281.2cm^3$

We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.

Answer 2

Answer:

Surface area $= 261.405 cm^2$

Volume of the cone $= 177.19 cm^3$

Step-by-step explanation:

Slant height of cone $= (r + \sqrt{r^2 + h^2})$

Height of the cone will be derived from this slant height

$14 = 4.5 + \sqrt{4.5^2 + h^2} \\9.5 = \sqrt{4.5^2 + h^2}\\90.25 = 20.25 + h^2\\h = 8.36$

Surface Area of Cone

$= \pi r (r + l)\\= (3.14) (4.5) (4.5 + 14)\\= 261.405$

Volume of the cone

$= \frac{1}{3} \pi r^2h\\= \frac{1}{3} (3.14)(4.5^2) (8.36)\\= 177.19 cm^3$