(1) A cone has height of 8cm and circular radius 6cm calculate (a) It's Volume (b) It's Slant Height (c) The Curved Surface Area (d) The Total Surface Area
r=3
use pythagoras to work out slant height (s) if h=8, ==> √(3^2+8^2)=s
pretty much plug in these values into the formula for a,c,d. Curved surface area is pi*r*s, don't count the base.
To find the volume, slant height, curved surface area, and total surface area of a cone, we can use the following formulas:
(a) Volume of a cone: V = (1/3) * π * r^2 * h,
(b) Slant height of a cone: l = √(r^2 + h^2),
(c) Curved surface area of a cone: A = π * r * l,
(d) Total surface area of a cone: A = π * r * (l + r).
Given:
h = 8 cm (height)
r = 6 cm (radius)
(a) Volume of the cone:
V = (1/3) * π * r^2 * h
= (1/3) * π * 6^2 * 8
= 301.59 cm^3 (approx)
(b) Slant height of the cone:
l = √(r^2 + h^2)
= √(6^2 + 8^2)
= √(36 + 64)
= √100
= 10 cm
(c) Curved surface area of the cone:
A = π * r * l
= π * 6 * 10
= 188.5 cm^2 (approx)
(d) Total surface area of the cone:
A = π * r * (l + r)
= π * 6 * (10 + 6)
= 226.2 cm^2 (approx)
So, the answers are:
(a) Volume = 301.59 cm^3
(b) Slant height = 10 cm
(c) Curved surface area = 188.5 cm^2
(d) Total surface area = 226.2 cm^2