Question

A spherical glass vessel has a cylinder neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345${\text{c}}{{\text{m}}^3}$. Check whether she is correct, taking the above as the inside measurements, and $\pi = 3.14$ .
A. Yes
B. No
C. Less data
D. None of these.

Answer 1

Hint: In this question, first make a diagram and write down the given data. Use the formula for volume of cylinder which is given by ${\text{V = }}\pi {{\text{r}}^2}h$ and then use the formula for finding volume of sphere which is given by ${\text{V = }}\dfrac{4}{3}\pi {{\text{r}}^3}$.

Complete step-by-step answer:

The diagram for the question is given below:

In the question it is given:
Length of cylindrical part = 8 cm
Diameter of cylindrical part = 2 cm
$\therefore $ Radius of cylindrical part = $\dfrac{2}{2} = 1$cm
Diameter of spherical part = 8.5 cm
$\therefore $ Radius of spherical part = $\dfrac{{8.5}}{2} = 4.25$cm.



Now, we know that volume of cylinder is given by:
Volume of cylinder = $\pi {{\text{r}}^2}h{\text{ c}}{{\text{m}}^3}$ (1)
Putting the values in equation 1, we get:
Volume of cylindrical part = $\pi {{\text{r}}^2}h{\text{ = 3}}{\text{.14}} \times {{\text{1}}^3} \times {\text{8 = 25}}{\text{.12 c}}{{\text{m}}^3}$ .
Also, , we know that volume of cylinder is given by:
Volume of sphere = $\dfrac{4}{3}\pi {{\text{r}}^3}{\text{ c}}{{\text{m}}^3}$ (2)
Putting the values in equation 2, we get:
Volume of cylindrical part = $\dfrac{4}{3}\pi {{\text{r}}^3}{\text{ = }}\dfrac{4}{3} \times {\text{3}}{\text{.14}} \times {4.25^3}{\text{ = 321}}{\text{.39 c}}{{\text{m}}^3}$
Now, volume of water in vessel = volume of spherical part + volume of cylindrical part
                                                   = ${\text{321}}{\text{.39 c}}{{\text{m}}^3}$ +${\text{25}}{\text{.12 c}}{{\text{m}}^3}$ =${\text{346}}{\text{.51 c}}{{\text{m}}^3}$ .
So approximately the child is correct that the capacity of the vessel is ${\text{345 c}}{{\text{m}}^3}$ .
Therefore, option A is correct.

Note: In this type of question, you should know that the volume of liquid in a vessel is equal to the volume of the vessel. You should remember the formula for calculating the volume of cylinder and volume of sphere.