+10 A solid consists of a right circular cone of height 12 cm surmounted on a right circular cylinder of the same height and radius 5 cm. Determine the total area and volume of a solid.
+128475 The cone will have 1/3 of the volume of the cylinder
The volume of the cylinder is pi * radius^2 * height = pi * (5)^2 * 12 = pi * 25 * 12 = 300 pi cm^3
So the volume of the cone is 300pi / 3 = 100 pi cm^3
So....the volume of the solid is [ 300 + 100] pi cm^3 = 400pi cm^3
The lateral area of the cylinder is 2pi * radius * height = 2pi * 5 * 12 = 120 pi cm^2
The area of the bottom of the cylinder is pi * radius^2 = pi * 5^2 = 25 pi cm^2
The slant height of the cone is √ [ height^2 + radius^2 ]= √ [12^2 + 5^2] =√169 = 13 cm
So....the lateral area of the cone is pi * radius * slant height = pi * 5 * 13 = 65 pi cm^2
So...the total area of the solid is [ 120 + 25 + 65] pi = 210 pi cm^2
