A cone has a volume of 98 cm³ - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 1

To find the height of the cone, we can rearrange the volume formula of a cone:

$V = \frac{1}{3} \pi r^2 h$

Given the volume ( V = 98 ) cm³ and radius ( r = 5.13 ) cm, we substitute these values into the formula:

$98 = \frac{1}{3} \pi (5.13)^2 h$

First, calculate ( (5.13)^2 ):

$(5.13)^2 \approx 26.33$

Now substituting back into the equation:

$98 = \frac{1}{3} \pi (26.33) h$

Multiplying both sides by 3 gives:

$294 = \pi (26.33) h$

Dividing both sides by ( \pi (26.33) ):

$h = \frac{294}{\pi (26.33)}$

Using an estimate for ( \pi \approx 3.14 ):

$h \approx \frac{294}{3.14 \times 26.33} \approx \frac{294}{82.67} \approx 3.56 \text{ cm}$

Thus, the height of the cone is approximately 3.56 cm.