Question

The diameter of a lead ball is 2.1 centimeter. The density of the lead used in 11.34 gm/cubic cm. What is the weight of the ball?

Answer 1

HINT:- Before solving this question, we must know about the formula used to calculate the volume of a sphere. Also, we must know about the formula to calculate the weight of any object.
Volume of sphere: \[=~\dfrac{4}{3}\pi {{r}^{3}}\], Weight: mg
Where, ‘m’ refers to the mass of the object and ‘g’ stands for acceleration due to gravity.

Complete step-by-step solution -
Firstly we will calculate the volume of the sphere.
Then, we shall multiply the volume of the sphere by the density of the lead ball.
By doing so, we will get the weight of the lead ball.

Diameter of the ball = 2.1 cm
Therefore, radius = \[\dfrac{2.1}{2}\] = 1.05 cm
We know that the formula to calculate the volume of a sphere,
\[=~\dfrac{4}{3}\pi {{r}^{3}}\]
Volume of the lead ball \[=\dfrac{4}{3}\times \dfrac{22}{7}\times 1.05\times 1.05\times 1.05\] = 4.851 cubic cm
Density of the lead of the lead ball = 11.34 g/ cubic cm
So, the weight of the lead ball \[=11.34~\times \text{ }4.851\] = 55.01 grams
Therefore, the weight of the ball made up of lead is 55.01 grams.
Hence, the answer of this question is 55.01 grams.

NOTE:- One must do all the calculations in this question very carefully.
Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.
\[\rho =\dfrac{m}{V}\] Where, \[\rho \] = density , \[m\] = mass and \[V\] =volume