Question

A drill cuts a hole of diameter 1 cm through a casting 7 cm thick. how much metal is removed?

Answer 1

Volume of metal removed = 5.5 cm²

Step-by-step explanation:

A drill cuts a hold of diameter 1cm in a cast of metal that is 7 cm thick.

The metal removed by the drill will be in the shape of a cylinder.

So the radius of the cylinder will be 1/2 = 0.5 cm and height of cylinder will be 7 cm.

Volume of metal removed = volume of cylinder = πr²h

= 22/7 * 0.5 * 0.5 * 7

= 5.5 cm²

Answer 2

Given:

• Hole of the diameter = 1cm.

• Height of casting = 7cm.

To Find:

• How much metal is removed = ?

Formula Used:

• Volume of cylinder = πr²h.

Solution:

Here,

(As, metal is removed, it will occupy a shape of Cylinder.)

i.e,

★ Radius of cylinder = ½ = 0.5cm.

We can derive that,

★ Metal removed = Volume of Cylinder.

Substituting values,

➙ 22/7 × (0.5)² × 7

➙ 22/7 × 0.25 × 7

➙ 22/7 × 1.75

➛ 5.5cm².

Hence,

• Total 5.5cm² metal is removed.

ExtraShots:

• Curved surface area of cylinder = 2πrh.

• Total Surface area of cylinder = 2πr (r + h).

• Volume of cylinder = πr²h.

• Surface area of sphere = 4πr².

• Volume of sphere = 4/3πr³.

• Surface area of cube = 4l².

• Total surface area of cube = 6l².

• Volume of cube = l³.