6.5.6 Volume of Three Dimensional Shapes, PT3 Practice - Mathematics

Question 14:
Diagram shows a right cylinder with a diameter of ( y + 4 ) cm.

Given the volume of the cylinder is 269.5 cm³ and by using find the value of it’s radius. [4 marks]

Solution:

volume of the cylinder = 269.5

πr²h = 269.5

\begin{array}{l} \frac{22}{7} \times r^{2} \times 7 = 269.5 \\ \frac{22}{7} \times {(\frac{y + 4}{2})}^{2} \times 7 = 269.5 \\ {(\frac{y + 4}{2})}^{2} = \frac{269.5}{22} \\ \frac{{(y + 4)}^{2}}{4} = 12.25 \\ (y + 4) = \sqrt{49} \\ y = 7 - 4 or - 7 - 4 \\ y = 3 or - 11 (n o t a c c e p t e d) \end{array}

$\begin{array}{l} \frac{22}{7} \times r^{2} \times 7 = 269.5 \\ \frac{22}{7} \times {(\frac{y + 4}{2})}^{2} \times 7 = 269.5 \\ {(\frac{y + 4}{2})}^{2} = \frac{269.5}{22} \\ \frac{{(y + 4)}^{2}}{4} = 12.25 \\ (y + 4) = \sqrt{49} \\ y = 7 - 4 or - 7 - 4 \\ y = 3 or - 11 (n o t a c c e p t e d) \end{array}$

Diameter ( y + 4 ) = 3 + 4 = 7

Therefore, radius of the cylinder = 3½ cm

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