Question

If the height and radius of a cone of volume V is doubled, find the new volume of the cone.

Answer 1

volume of new cone=1/3*22/7*(2r)^2*2h
                                =176r^2h/21
                                =8.38cubic units

Answer 2

$\huge\mathbb{SOLUTION:-}$

$\boxed{\sf{Volume\:of\:cone=\dfrac{1}{3} \pi r{}^{2}h}}$

Now we have

• r= 2r

• h= 2h

Now the Volume

$\sf:\implies Volume=\dfrac{1}{3} \pi r{}^{2} h\\ \\ \sf:\hookrightarrow r=2r \:\:and\:\:h=2h\\ \\ \sf:\implies Volume=\dfrac{1}{3}\times \pi \times (2r){}^{2}\times 2h\\ \\ \sf:\implies Volume=\dfrac{1}{3} \pi \times 4r{}^{2}\times 2h\\ \\ \sf:\implies Volume= 8 (\dfrac{1}{3} \pi r{}^{2}h)$

• Now the Volume of new cone

$\boxed{\sf{Volume\:of\:new\:cone=8\times (Volume\:of\:old) }}$