(a) (i) Find the volume of a solid sphere of radius 0.3 cm - Leaving Cert Mathematics - Question 9 - 2018

The mass of pure gold in the sphere can be calculated using the density of pure gold, which is 19.3 grams/cm³: $\text{Mass} = \text{Volume} \times \text{Density}$ Substituting the known values: $\text{Mass} = 0.113 \text{ cm}^3 \times 19.3 \text{ g/cm}^3$ Calculating this gives: $\text{Mass} \approx 2.18 \text{ grams}$ Thus, the answer correct to two decimal places is 2.18 grams.

To find the number of atoms, we first find the number of grams in 197 grams of gold, which corresponds to approximately 6.02 × 10²³ atoms: Using the mass calculated earlier (2.18 grams): $\text{Number of atoms} = \left( \frac{6.02 \times 10^{23} \text{ atoms}}{197 \text{ grams}} \right) \times 2.18 \text{ grams}$ Calculating this: $\text{Number of atoms} \approx 6.67 \times 10^{21}$ Thus, the answer in the required form is: 6.67 × 10²¹.