Question

A solid metallic cone of radius 6 cm and height 12 cm is melted 2 shaped into 36 cones of radius 2 cm.find their height.

Answer 1

Answer:

Height of the new cones = 3 cm

Step-by-step explanation:

Volume of big cone = 36 * volume of small cones

1/3*pi*R²*H = 36 * 1/3*pi * r² *h;

1/3*pi*6*6*12 = 12*pi*2*2*h;

144*pi = 48*pi*h;

144 = 48*h;

h = 3;

height of small cone = 3 cm

Answer 2

$\bold\blue{Correct \ Question}$

$\sf{A \ solid \ metallic \ cone \ of \ radius}$

$\sf{6 \ cm \ and \ height \ 12 \ cm \ is \ melted}$

$\sf{to \ shaped \ into \ 36 \ cones \ of \ radius}$

$\sf{2 \ cm. \ Find \ their \ height.}$

$\red{\underline{\underline{Answer:}}}$

$\sf{The \ height \ of \ the \ cones \ will \ be}$

$\sf{4 \ cm}$

$\orange{\underline{\underline{Given:}}}$

$\sf{For \ sold \ metallic \ cone,}$

$\sf{\implies{Radius (r)=6 \ cm}}$

$\sf{\implies{Height (h)=12 \ cm}}$

$\sf{For \ cones \ formed \ after \ melting,}$

$\sf{\implies{Radius (R)=2 \ cm}}$

$\pink{\underline{\underline{To \ find:}}}$

$\sf{Height (H) \ of \ cones \ formed \ after}$

$\sf{melting.}$

$\green{\underline{\underline{Solution:}}}$

$\sf{Volume \ of \ cone=\frac{1}{3}\times\pi\times \ r^{2}\times \ h}$

$\sf{...formula}$

$\sf{36 \ cones \ are \ formed \ by \ melting \ cone.}$

$\sf{Hence, \ their \ volume \ will \ be \ same.}$

$\sf{\therefore{\frac{1}{3}\times\pi\times \ r^{2}\times \ h=36\times\frac{1}{3}\times\pi\times \ R^{2}\times \ H}}$

$\sf{6^{2}\times12=36\times2^{2}\times \ H}$

$\sf{\therefore{H=\frac{12}{4}}}$

$\sf{\therefore{H=3 \ cm}}$

$\sf\purple{\tt{\therefore{The \ height \ of \ the \ cones \ will \ be}}}$

$\sf\purple{\tt{4 \ cm}}$