Mathematics Questions and Answers

Volume of a cylinder = πr\(^2\)h

First convert 3m to cm by multiplying by 100

Volume of External cylinder = π \times 13\(^2\) \times 300

Volume of Internal cylinder = π \times 10\(^2\) \times 300

Hence; Volume of External cylinder - Volume of Internal cylinder

Total volume (v) = π (169 - 100) \times 300

V = π \times 69 \times 300

V = 20700πcm\(^3\)

Cos \(\theta\) = \(\frac{12}{13}\)

x² + 12² = 13²

x² = 169- 144 = 25

x = 25

= 5

Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\)

If cos²\(\theta\) = 1 + \(\frac{1}{tan^2\theta}\)

= 1 + \(\frac{1}{\frac{(5)^2}{12}}\)

= 1 + \(\frac{1}{\frac{25}{144}}\)

= 1 + \(\frac{144}{25}\)

= \(\frac{25 + 144}{25}\)

= \(\frac{169}{25}\)

For a regular polygon of n sides

n = \(\frac{360}{\text{Exterior angle}}\)

Exterior < = 180° - 140°

= 40°

n = \(\frac{360}{40}\)

= 9 sides

The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices.

A rhombus has two diagonals that bisect each other at right angles.

i.e this splits 6cm into 3cm each AND 8cm to 4cm

Using Hyp\(^2\) = adj\(^2\) + opp\(^2\)

Hyp\(^2\) = 3\(^2\) + 4\(^2\)

Hyp\(^2\) = 25

Hyp = 5

∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths

Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)

= \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm

Perimeter = 8.8 + 2r

= 8.8 + 2(10.5)

= 8.8 + 21

= 29.8cm