Higher November 2022 Paper 1 Q24
24 Here is a solid sphere and a solid cone.
All measurements are in cm.
The volume of the sphere is equal to the volume of the cone.
(a) Find \(r : h\)
Give your answer in its simplest form. (2)
Give your answer in its simplest form. (2)
Here is a different solid sphere and a different solid cone.
All measurements are in cm.
The surface area of the sphere is equal to the total surface area of the cone.
(b) Find \(r : h\)
Give your answer in the form \(1 : \sqrt{n}\) where \(n\) is an integer. (4)
Give your answer in the form \(1 : \sqrt{n}\) where \(n\) is an integer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1 : 4 | P1 | for process to equate the two volumes, \(\dfrac{4}{3}\pi r^3 = \dfrac{1}{3}\pi r^2 h\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(1 : \sqrt{8}\) | P1 | for process to equate surface areas, eg \(4\pi r^2 = \pi r^2 + \pi rl\) |
| P1 | for process to substitute \(l = \sqrt{h^2 + r^2}\), eg \(4\pi r^2 = \pi r^2 + \pi r\sqrt{h^2 + r^2}\) | |
| P1 | for process to isolate term in \(r^2\) after substituting for \(l\), eg \(8r^2 = h^2\) | |
| A1 | for \(1 : \sqrt{8}\) |
Additional guidance
Can be implied by \(3r = l\)