Question
2. A snooker ball is a sphere with a diameter of 5.2 cm. (a) Calculate the volume of the snooker ball. The density of an object can be calculated using the formula below. Density=(mass)/(volume) The mass of the snooker ball is 142 grams. (b) Calculate the density of the snooker ball. Give your answer in grams per cubic centimetre.
Answer
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Kirk
Professional · Tutor for 6 years
Answer
## Step 1: Calculation of Volume.The diameter of the snooker ball is
, so the radius is
. Substituting this into the volume formula gives:### \(V = \frac{4}{3} \pi (2.6)^3 \approx 73.2 \, \text{cm}^3\)## Step 2: Calculation of Density.The mass of the snooker ball is
and the volume is
. Substituting these values into the density formula gives:###
Therefore, the volume of the snooker ball is approximately
and the density is approximately
.
Explanation
## Step 1: Calculation of Volume.The volume of a sphere can be calculated using the formula
, where
is the radius of the sphere. However, we are given the diameter of the snooker ball, which is twice the radius. Therefore, we first need to calculate the radius by dividing the diameter by 2. ###
After finding the radius, we can substitute it into the volume formula to find the volume of the snooker ball.###
## Step 2: Calculation of Density.The density of an object can be calculated using the formula
, where
is the mass and
is the volume. We are given the mass of the snooker ball and we have calculated the volume in the previous step. Therefore, we can substitute these values into the density formula to find the density of the snooker ball.###