Question

Aumentando de 1/5 o raio da base de um cone circular reto e reduzindo em 1/5 sua altura, o seu volume

Answer 1

$\large\boxed{\begin{array}{l}\rm volume\,do\,cone\,original:V=\dfrac{1}{3}\cdot \pi\cdot r^2\cdot h\\\rm\dfrac{1}{5}=0,2\\\rm aumentando\,o\,raio\,em\,\dfrac{1}{5}:1,2\cdot r\\\rm diminuindo\,a\,altura\,em\,\dfrac{1}{5}:0,8\cdot h\\\rm c\acute alculo\,do\,novo\,volume:\\\rm V_{novo}=\dfrac{1}{3}\cdot\pi\cdot(1,2r)^2\cdot0,8h\\\\\rm V_{novo}=\dfrac{1}{3}\cdot\pi\cdot1,44r^2\cdot 0,8h\\\\\rm V_{novo}=115,2\cdot\dfrac{1}{3}\cdot \pi\cdot r^2\cdot h\\\rm V_{novo}=115,2\cdot Volume_{original}\end{array}}$

$\large\boxed{\begin{array}{l}\rm Conclus\tilde ao:\\\sf aumentando-se\,o\,raio\,em\,\dfrac{1}{5}\,e\, diminuindo\,a\,altura\,em\,\dfrac{1}{5}\\\\\sf o\,volume\,tem\,um\,aumento\,de\,15,2\%\end{array}}$