Question

A pencil consists of a cone stacked on top of a cylinder. The diameter of the cylindrical base of the pencil is 10 mm and the height of the cylinder is 70 mm, while the height of the cone is 12 mm. Calculate the surface area of the pencil. Leave your answer in terms of π.

Answer 1

Answer:

$790\pi\,\,mm^2$

Step-by-step explanation:

Given: The diameter of the cylindrical base of the pencil is 10 mm and the height of the cylinder is 70 mm, while the height of the cone is 12 mm

To find: surface area of the pencil

Solution:

Radius of the cone = Radius of the cylinder (r) = diameter/2 = $\frac{10}{2}=5\,\,mm$

Height of the cylinder (H) = 70 mm

Height of the cone (h) = 12 mm

Slant height of the cone (l) = $\sqrt{r^2+h^2}=\sqrt{5^2+(12)^2}=\sqrt{25+144}=\sqrt{169}=13\,\,mm$

Curved surface area of cone = $\pi rl=\pi (5)(13)=65\,\pi \,\,mm^2$

Surface are of cylinder = curved surface area of cylinder + base area of cylinder

$=2\pi rH+\pi r^2\\=\pi r(2H+r)\\=\pi(5)\left [ 2(70)+5 \right ]\\=5 \pi\left ( 140+5 \right )\\=725\pi\,\,mm^2$

So,

surface area of the pencil = Curved surface area of cone + Surface are of cylinder = $65\pi+725\pi=790\pi\,\,mm^2$