Question

A circular cone has a height of 17mm and a slant height of 21 mm. Find the volume and the total surface area 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

Answer 2

tsa formula =pie×r×l

volume =pie×r^2×h/3