Question

The portion of a student’s ballpoint pen that contains the ink is a cylinder with a diameter of 0.400 cm and a height of 11.5 cm. If the ink lasts 7 weeks, what is the volume of ink that the student uses each week?

A) 0.21 cm3.
B) 0.92 cm3.
C) 1.84 cm3.
D) 12.9 cm3.

Answer 1

The answer to this question is A.

Answer 2

Option A is correct

0.21
`\text{cm}^3`

Explanation:

Volume of a cylinder(V) is given by:

`V = \pi r^2h`

where,

r is the radius and h is the height of the cylinder respectively.

As per the statement:

The portion of a student’s ballpoint pen that contains the ink is a cylinder with a diameter of 0.400 cm and a height of 11.5 cm.

⇒diameter(d) = 0.400 cm and height(h) = 11.5 cm

We know that:

Diameter(d) = 2(r)

then;

`0.400 = 2r`

Divide both sides by 2 we have;

`0.200 = r`

or

r = 0.200 cm

Using the formula [1] substitute the given values we have;

`V = 3.14 \cdot (0.200)^2 \cdot 11.5`

Simplify:

V = 1.4444 cubic cm.

It is given that If the ink lasts 7 weeks.

then;

Volume of ink that the student uses each week =
`(1.4444)/(7) \approx 0.21  cm^3`

therefore, 0.21 cubic cm is the volume of ink that the student uses each week