Photo AI
A solid metal sphere has mass 235 g - OCR - GCSE Maths - Question 12 - 2021 - Paper 1
Question 12
A solid metal sphere has mass 235 g. The density of the metal is 7.78 g/cm³. Show that the surface area of this sphere is 46.9 cm², correct to 3 significant figures... show full transcript
Worked Solution & Example Answer:A solid metal sphere has mass 235 g - OCR - GCSE Maths - Question 12 - 2021 - Paper 1
Step 1
Calculate the volume of the sphere
Answer
To find the radius of the sphere, we first use the mass and the density to calculate the volume.
Using the formula for density:
[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} ]
We rearrange it to find volume:
[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{235 \text{ g}}{7.78 \text{ g/cm}^3} \approx 30.17 \text{ cm}^3 ]
Step 2
Determine the radius of the sphere
Answer
Using the volume formula for a sphere:
[ V = \frac{4}{3} \pi r^3 ]
We can solve for radius r:
[ 30.17 = \frac{4}{3} \pi r^3 ]
Rearranging gives:
[ r^3 = \frac{30.17 \times 3}{4\pi} \approx 7.19 ]
Taking the cube root, we find:
[ r \approx 1.95 \text{ cm} ]
Step 3
Calculate the surface area of the sphere
Answer
Now, using the formula for the surface area of a sphere:
[ A = 4 \pi r^2 ]
We substitute the value of r:
[ A = 4\pi (1.95)^2 \approx 46.9 \text{ cm}^2 ]
This confirms that the surface area is approximately 46.9 cm², correct to 3 significant figures.