A right-angled triangle is rotated about its perpendicular. If the perpendicular, hypotenuse and base of the triangle are 8 cm, 10 cm and 6 cm respectively, find the volume of the cone formed through rotation. (\(\pi=3.14\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 301.44 cm3
When a right-angled triangle turns about one of the sides containing the right angle, that side becomes the height of the cone and the other one its radius; the hypotenuse becomes the slant height. Here the triangle turns about its perpendicular.
Height \(h=8\) cm (the perpendicular), radius \(r=6\) cm (the base)
\(\displaystyle V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times3.14\times6\times6\times8\)
\(=3.14\times96=301.44\,\mathrm{cm^3}\)