Question

A Conical ice creams jar of top diameter 7cm is 10cm deep. What is the capacity in liters?

Answer 1

- Hint: In this question we are going to calculate the capacity of conical ice cream jar that is the volume of the jar by putting the value of the radius and height of the conical jar in the formula for calculating volume of jar and then converting the volume in liters. And the formula is written below.

Formula Used:
The formula for calculation volume of cone is =$\dfrac{1}{3}\pi {r^2}h$
Where r is the radius of the cone and h is the height of the cone
And the value of pie is taken as 22/7.
For converting the volume into liters we use the conversion
$1c{m^3} = 0.001litre$

Complete step-by-step solution -

Firstly we will calculate the value of radius of conical ice cream jar
For that we know that radius is half of diameter
That is,
$r = \dfrac{d}{2}$
Now putting the value of diameter as given in the problem that is 7 cm
Putting we get,
$r = \dfrac{7}{2}$
Now dividing 7 by 2 we get,
$r = 3.5cm$
Now we have the value for radius and we have the value of height that is given in problem as 10 cm
Now putting the values in above formula for calculation volume of conical ice cream jar we get,
=$0.12833litres$ $\dfrac{1}{3}\pi {(3.5)^2}(10)$
Now, putting the value of pie as 22/7 we get,
=$\dfrac{1}{3}(\dfrac{{22}}{7}){(3.5)^2}(10)$
Now calculating the square of 3.5 by multiplying to it we get,
=$\dfrac{1}{3}(\dfrac{{22}}{7})(12.25)(10)$
Now, multiplying the above numerator terms that is 22 multiplied by 12.27 and 10 we get,
=$\dfrac{{2695}}{{3 \times 7}}$
Now multiplying 7 and 3 in the denominator we get,
=$\dfrac{{2695}}{{21}}$
Now dividing 2695 by 21 that is numerator by denominator we get,
=$128.33c{m^3}$
Hence the volume of the conical ice cream jar is $128.33c{m^3}$
Now converting the above volume in liters by using the conversion stated above
$1c{m^3} = 0.001litre$
Now, multiplying above equation by$128.33c{m^3}$ we get
$128.33c{m^3}$= $128.33 \times 0.001litre$
Now multiplying we get,
=$0.12833litres$

Hence, we find the capacity of conical ice cream jar in litres that is $0.12833litres$

Note:
Use a proper formula for calculating the volume of cones. And to analyze what is given in the question to find the desired output. By seeing the question you should be careful in which units the answer is wanted, so by using proper conversion you get the answer in proper units.
One may get a slightly different answer whenever it uses the value of pi as 3.14 so for that always use the value of pie as 22/7 to get the proper accurate answer.