Question

plzz do que no 76......​

Answer 1

Solution:

Given:

=> Height of cone = 7 cm.

=> Diameter of cone = Diameter of hemisphere = 14 cm.

=> Radius of cone = Radius of hemisphere = 14/2 = 7 cm.

To find:

=> Volume of toy.

=> Difference of the volume of the cylinder and the toy.

Formula used:

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

$\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3} \pi r^{3}}$

$\sf{\implies Volume\;of\;cylinder=\pi r^{2}h}$

So, first will we find volume of cone.

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

$\sf{\implies Volume\;of\;cone=\dfrac{1}{3}\pi \times (7)^{2}\times 7}$

$\sf{\implies Volume\;of\;cone=\dfrac{343\pi}{3}\;cm^{3}}$

Now, we will calculate volume of hemisphere.

$\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3} \pi r^{3}}$

$\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3}\times \pi \times (7)^{3}}$

$\sf{\implies Volume\;of\;hemisphere=\dfrac{686 \pi}{3}\;cm^{3}}$

$\sf{Now,\;volume\;of\;toy=Volume\;of\;cone+Volume\;of\;hemisphere}$

$\sf{\implies volume\;of\;toy=\dfrac{343 \pi}{3} +\dfrac{686 \pi}{3}}$

$\sf{\implies volume\;of\;toy=\dfrac{343 \pi+686 \pi}{3}}$

$\sf{\implies volume\;of\;toy=\dfrac{1029 \pi}{3}}$

$\sf{\implies volume\;of\;toy=\dfrac{1029\times 3.14}{3}}$

$\sf{\implies volume\;of\;toy=\dfrac{3231.06}{3}}$

$\sf{\implies volume\;of\;toy=1077.02\;cm^{3}}$

Hence, volume of toy is 1077.02 cm³.

Now, we will find the difference of the volume of the cylinder and the toy.

$\sf{\implies Volume\;of\;cylinder=\pi r^{2}h}$

Where,

=> Radius of cylinder = radius of cone = 7 cm.

=> Height of cylinder = Height of cone + radius of hemisphere.

=> Height of cylinder = 14 cm

Now, put the values in the formula.

$\sf{\implies Volume\;of\;cylinder=\pi r^{2}h}$

$\sf{\implies Volume\;of\;cylinder=3.14\times (7)^{2}\times 14}$

$\sf{\implies Volume\;of\;cylinder=2154.04\;cm^{3}}$

Now, Difference in the volume = Volume of cylinder - Volume of toy

=> Difference in the volume = 2154.04 cm³ - 1077.02 cm³

=> Difference in the volume = 1077.02 cm³

Hence, Difference in the volume = 1077.02 cm³.