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.

835π sq. mm.
790π sq. mm.
785π sq. mm.
1820π sq. mm.

Answer 1

ANSWER:

Given:

• Pencil consists of a cone atop a cylinder.
• Diameter of cylindrical base = 10mm
• Height of cylinder = 70mm
• Height of cone = 12mm

To Find:

• Surface Area of the pencil

Solution:

We are given that,

⇒Diameter of the cylindrical base = 10mm

So,

⇒Radius of the cylindrical base = 5mm

Now, we need to find the Surface Area of the pencil.

For that, we will find the Area of the cylindrical base, Lateral Surface Area of the cylinder and the Lateral Surface Area of the cone and add all the three areas.

That is,

⇒Surface Area of the pencil = Area of the cylindrical base + Lateral Surface Area of the cylinder + Lateral Surface Area of the cone

We know that,

⇒Area of cylindrical base = πr²,

⇒Lateral Surface Area of cylinder = 2πrh, and

⇒Lateral Surface Area of cone = πrl = πr√(r² + H²)

So,

⇒Surface Area of the pencil = πr² + 2πrh + πr√(r² + H²)

Here, r = 5mm, h = 70mm, H = 12mm.

So,

⇒Surface Area of the pencil = π[5² + 2(5)(70) + 5√(5² + 12²)]

⇒Surface Area of the pencil = π[25 + 700 + 5√(25 + 144)]mm²

⇒Surface Area of the pencil = π[725+ 5√(169)]mm²

⇒Surface Area of the pencil = π[725+ 5(13)]mm²

So,

⇒Surface Area of the pencil = π[725+ 65]mm²

Hence,

⇒Surface Area of the pencil = 790π mm²

Therefore, the Surface Area of the pencil is (option b) 790π sq. mm