Calculate the volume and the total surface area of a cone of base 16cm and slant height of 17cm

Answer 1

Need the vertical height, not slant height, but
h^2 + 8^2 = 17^2
h = √225 = 15

vol = (1/3)π r^2 h = (1/3)π(64)(15) = 320π cm^3
SA = circular base + surface of cone
= π(8^2) + π r l, where l is the slant height
= 64π + π(8)(17) = 200π cm^2

Answer 2

Calculate the volume and the total surface area of a cone of base diameter 16cm and slant height 17cm in terms of pie

Answer 3

To find the height of the cone, we need to use the Pythagorean theorem:

h^2 + 8^2 = 17^2

h^2 = 17^2 - 8^2

h^2 = 225

h = 15cm

The radius of the base is half the diameter, so r = 8cm.

The volume of the cone is:

V = (1/3)πr^2h

V = (1/3)π(8^2)(15)

V = 320π/3 cubic cm

To find the total surface area, we need to add the area of the base to the lateral surface area.

The area of the base is:

A_base = πr^2

A_base = π(8^2)

A_base = 64π square cm

The lateral surface area (or curved surface area) can be found using the slant height:

A_lateral = πrl

A_lateral = π(8)(17)

A_lateral = 136π square cm

The total surface area is:

A_total = A_base + A_lateral

A_total = 64π + 136π

A_total = 200π square cm