4400 Higher November 2007 Paper 4 Q26

EdexcelHigherOld spec5 marksVolume & Surface Area

Solid made of a cone of height r on top of a cylinder of height r, both of radius r

The diagram shows a solid made from a cone and a cylinder.
The cylinder has radius \(r\) and height \(r\).
The cone has base radius \(r\) and height \(r\).

(a) Show that the total volume of the solid is equal to the volume of a sphere of radius \(r\). (2)

The curved surface area of a cylinder with base radius \(r\) and height \(h\) is \(2\pi rh\).
The curved surface area of a cone with base radius \(r\) and slant height \(l\) is \(\pi rl\).

(b) Show that the total surface area of the above solid is greater than the surface area of a sphere of radius \(r\). (3)

Scheme	Marks
\(\frac{1}{3}\pi r^2 \times r + \pi r^2 \times r\) or \(\frac{1}{3}\pi r^3 + \pi r^3\)	M1
\(\frac{4}{3}\pi r^3\)	A1
	(2)

Scheme	Marks
\(\pi rl + 2\pi r^2 + \pi r^2\) oe	M1
\(l \gt r\) or \(l = r\sqrt{2}\) oe	M1
\(\gt 4\pi r^2\)	A1
	(3)
	(5 marks)

Notes