A solid cone has base radius 7 cm, perpendicular height \(h\) cm and slant height \(l\) cm
\[\text{Curved surface area of a cone} = \pi r l\]
The total surface area of the cone is \(224\pi\) cm\(^2\)
Work out the size of the angle between the slant height and the base. [4 marks]
(b)
\(ABCDEFGH\) is a cuboid.
\(ABCD\) is horizontal.
\(MN\) is vertical.
The acute angle between the planes \(MNB\) and \(HDCG\) is \(36^\circ\)
Work out the length \(CN\). [2 marks]
Mark scheme (a)
Answer
Mark
Comments
Alternative method 1: works out value for slant height
\(224\pi - \pi \times 7 \times 7\) or \(175\pi\) or \(224 - 7 \times 7 = 7l\) or \(175 = 7l\)
M1
oe curved surface area accept a value [3.14, 3.142] for \(\pi\) eg \(224 \times 3.14 - 3.14 \times 49\) or oe equation with \(7l\) as the subject eg \(7l = 224 - 49\)
\((224\pi - \pi \times 7 \times 7) \div (\pi \times 7)\) or \(175 \div 7\) or 25
\(\cos x = \dfrac{7}{\text{their } 25}\) or \(\cos x = 0.28\) or \(\cos^{-1}\dfrac{7}{\text{their } 25}\) or \(\cos^{-1} 0.28\)
M1dep
oe eg \(\sin x = \dfrac{\sqrt{\text{their } 25^2 - 7^2}}{\text{their } 25}\) or \(\sin x = 0.96\) or \(\tan x = \dfrac{\sqrt{\text{their } 25^2 - 7^2}}{7}\) or \(\tan x =\) [3.4, 3.43]
[73.7, 73.74]
A1
accept 74 with correct method seen SC2 [76.5, 76.51] or [77.3, 77.4]
Alternative method 2: works out expression for slant height
