Question

A shot putt is a metallic sphere of radius 4.9cm. If the density of the metal is 7.8 gm per cubic cm, find the mass of the shot putt.

Answer 1

Hint: To solve this question we will use a formula relating the density of a substance to its mass and volume. The formula is stated as \[\text{Density of substance}=\dfrac{\text{Mass }}{\text{Volume}}.\] We are given that the radius of the metallic shot put ball is 4.9cm. Let the radius be r. Therefore, r = 4.9cm. Because the metallic ball is in the form of a sphere so the radius r is of the sphere.

Complete step-by-step solution:
We are given that the density of the sphere metallic ball is 7.8g cubic cm. Let it be D = 7.8 cubic cm. Using the formula of density relating mass and volume stated as
\[\text{Density}=\dfrac{\text{Mass }}{\text{Volume}}\]
\[\Rightarrow D=\dfrac{Mass}{V}\]
Where D is the density and V is the volume.

Now, we need to determine the volume V of the sphere using its radius r. The volume of the sphere is \[V=\dfrac{4}{3}\pi {{r}^{3}}.\] Substituting r = 4.9 cm, we have the volume of the sphere as
\[V=\dfrac{4}{3}\pi {{\left( 4.9 \right)}^{3}}\]
Putting \[\pi =\dfrac{22}{7},\] we get,
\[\Rightarrow V=\dfrac{4}{3}\times \dfrac{22}{7}\times {{\left( 4.9 \right)}^{3}}\]
\[\Rightarrow V=493.0053\]
So, we have the volume of the sphere, V = 493.0053.
Substituting the volume obtained in the above formula, we have,
\[\text{Density}=\dfrac{\text{Mass }}{\text{Volume}}\]
\[\Rightarrow 7.8=\dfrac{Mass}{493.0053}\]
\[\Rightarrow Mass=7.8\times 493.0053\]
\[\Rightarrow Mass=3845.441gm\]
\[\Rightarrow Mass=3.845kg\]
Hence, the mass of the shot putt is 3.845 kg.

Note: We have used the conversion formula of a gram into kilograms as 1kg = 1000 grams. We have obtained the final value as
\[3845.441gram=3845.441\times \dfrac{1}{1000}\]
\[\Rightarrow 3845.441gram=3.845kg\]
Hence, the result.