18. Is the volume of the cylinder with radius 14.1 cm and height 18 cm greater than that of the cone with radius 14.8 cm and height 17.5 cm? Show your working clearly. - OCR - GCSE Maths - Question 19 - 2020 - Paper 1

The volume ( V ) of a cone is given by the formula: $V = \frac{1}{3} \pi r^2 h$ For the cone:

• Radius ( r = 14.8 \text{ cm} )
• Height ( h = 17.5 \text{ cm} )

Substituting the values in: $V = \frac{1}{3} \pi (14.8)^2 (17.5)$ Calculating: $V \approx \frac{1}{3} \times 3.14 \times 219.04 \times 17.5 \approx 1276.26 \text{ cm}^3$

Now, we compare the volumes:

• Volume of Cylinder: ( \approx 11334.23 \text{ cm}^3 )
• Volume of Cone: ( \approx 1276.26 \text{ cm}^3 )

Since ( 11334.23 \text{ cm}^3 > 1276.26 \text{ cm}^3 ), it is clear that the volume of the cylinder is greater than that of the cone.