Question

A conical cup has a circular base with a diameter of 21cm and height 1.8dm. How much oil can it contain?

Answer 1

Hint: Here we have to find the content of the conical cup which has a diameter of 21 cm and a height of 1.8 dm. For this, just find the volume of the cone after the conversion of height in centimeters.

Complete step-by-step answer:

We know that, 1 dm = 10 cm.
Now it is given the height of the cup is 1.8dm, we will convert it into cm, so we get
1.8 dm = 10 (1.8) cm = 18 cm.
Now we also know, diameter = 2 * radius,
And in question, we are given the diameter which is equal to 21 cm.
So the radius of the conical cup will be r = 10.5 cm.
The height of the cup is,
h=1.8 dm=18 cm.
Now we know the formula of the volume as,
Volume = \[\dfrac{1}{3}\pi {{r}^{2}}h\]
Substituting the radius and height of the cup, we get the volume as
\[\begin{align}
  & =\dfrac{1}{3}\times \dfrac{22}{7}\times 10.5\times 10.5\times 18 \\
 & =2079\,c{{m}^{3}}. \\
\end{align}\]
We know that
\[1c{{m}^{3}}=1ml\]
Hence the amount of oil it contained in the conical cup is 2079ml.

Note: In this question, students can make a mistake by directly multiplying the height which is given in ‘dm’ with radius during finding volume.So, first convert the given height into centimeters and then find the volume of the cup which has a conical shape.