A cone has a radius of $(1+\sqrt{2})$ cm and a volume of $(7+4\sqrt{2})\pi$ cm${}^3$. Without

Question

A cone has a radius of $(1+\sqrt{2})$ cm and a volume of $(7+4\sqrt{2})\pi$ cm${}^3$. Without using a calculator, find the height of the cone, in cm, in the form $(a+b\sqrt{2})$, where $a$ and $b$ are integers. [The volume of a cone of radius $r$ and height $h$ is $\frac{1}{3}\pi r^2 h$.][4]

Accepted Answer

$h=15-6\sqrt2\text{ cm}$, so $a=15$, $b=-6$

2023 ACSBR AM S3 EOY Q2

2023 ACSBR AM S3 EOY Q2

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