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Question
If the radius of the base of a cone is tripled and the height is doubled then the volume is
Options
made 6 times
made 18 times
made 12 times
unchanged
Solution
made 18 times
Explanation;
Hint:
Radius of a cone = r
Height of a cone = h
Volume of the cone = `1/3` πr2h cu.units
When the radius is increased three-time (tripled) and the height is doubled
Radius is 3r and the height is 2h
Volume of the new cone
= `1/3 pi(3pi)^2 xx 2"h"`
= `1/3 pi xx 9pi^2 xx 2"h"`
= `1/3 pi"r"^2"h" (18)`
Volume is increased 18 times.
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