A solid S is made up of a cylindrical part and conical part. The height of the Soild is 4.5m. The common radius of the cylindrical part and the conical part is 0.9m. The height of the conical part is 1.4m.

Question

a. Calculate the volume,correct to 1 decimal place,of soild S.

b. Calculate the total surface area of soild S.

c. A square base pillar offside 1.6m has the same volume as soild S. Determine the height of the pillar, correct to 1 decimal place.

Answer 1

r is cylinder radius and the radius of the base of the cone
H is the cylinder height
h is the cone height

The volume of a cylinder is the height times the base area
Vcyl = pi r^2 H
The volume of a anything with straight sides and apointy top is (1/3)base area*height
so
Vcone = (1/3) pi r^2 h

add them
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the surface area of the sides of a cylinder is 2 pi r H
the surface area of the bottom of the cylinder is pi r^2
the surface area of a cone is (1/2)perimeter * slant height
slant height = sqrt (r^2+h^2)
perimeter = 2 pi r
so total area = 2 pi rH + pi r^2 + (1/2)(2 pi r)(sqrt(r^2+h^2)

Answer 2

1.6^2 * height = that volume you got in part a above