Higher June 2023 Paper 1 Q16
16 Here is a sphere.
\(\dfrac{3}{8}\) of the surface area of this sphere is \(75\pi\) cm2
Find the diameter of the sphere.
Give your answer in the form \(a\sqrt{b}\) where \(a\) is an integer and \(b\) is a prime number. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(10\sqrt{2}\) | P1 | for process to find total surface area of sphere, eg \(75\pi \div 3 \times 8\ (= 200\pi)\) or \(75 \div 3 \times 8\ (= 200)\) or for setting up an equation, eg \(\dfrac{3}{8} \times 4\pi r^2 = 75\pi\) or \(\dfrac{3}{8} \times 4r^2 = 75\) |
| P1 | for process to find \(r^2\), eg \((r^2 =)\ \dfrac{\text{``}200\pi\text{''}}{4\pi}\) oe or \((r^2 =)\ \dfrac{75\pi}{4\pi} \times \dfrac{8}{3}\) oe or \(r^2 = \text{``}50\text{''}\) | |
| P1 | for process to find radius, eg \((r =)\ \sqrt{\dfrac{\text{``}200\pi\text{''}}{4\pi}}\) oe or \(\sqrt{\text{``}50\text{''}}\) or \(5\sqrt{2}\) or for \((2r =) = \sqrt{\text{``}200\text{''}}\) | |
| A1 | cao |
Additional guidance
Could work without \(\pi\) for the three P marks