In a cone with a slant height of 7.5 feet the slant height forms a 38 degree angle with the radius Find the surface area and volume of the cone?

Answer 1

If you unroll the cone you'll have a sector of a circle, where:

i) radius of the sector = slant height of the cone,

ii) arc length of the sector = circumference of the cone base.

From i)

l=r=7.5

From ii)

Arc length = AL=angle/360 x 2 x pi x r = 2 x pi x R

where r = radius of the sector and R = radius of cone base

Angle = 360 degree - 38 degree = 322 degree

so:

R = (322 x 7.5) / 360 = 6.71 feet

Height of the cone:

l^2 = H^2 + r^2 (Pythagoras Theorem)

H = 3.35 feet

So,

Volume = (pi x R^2 x H) / 3

Volume = 1577.87 feet^3

I hope this can help,

Luciana Melo

If you unroll the cone you'll have a sector of a circle, where:

i) radius of the sector = slant height of the cone

ii) arc length of the sector = circumference of the cone base

From i)

l = r = 7.5 feet

From ii)

Arc length = AL = angle/360 x 2 x pi x r = 2 x pi x R

Where:

r = radius of the sector

R = radius of cone base

angle = 360 degree - 38 degree = 322 degree

Height of the cone:

l^2 = H^2 + r^2

H = 3.35 feet

So, Volume:

V = (pi x R^2 x H)/3

V = 157.87 feet^3

I hope this can help,

Luciana Melo