Question

please give me answer of maths question 2​

Answer 1

Given :

A vessel is in the form of an inverted cone, it's height is 8cm and radius of its top which is open is 5cm. It is filled with water upto the brim. When lead shots each of which is sphere of radius 0.5cm are dropped into the vessel one fourth of the water flows out.

To find :

We should find the number of lead shots dropped into the vessel.

Explaination :

In an inverted cone of height and radius 8cm and 5cm, water is filled to it's brim. Here, a few lead shots of radius 0.5cm are dropped into the cone. When they are dropped into the water, one-fourth of the water flows out. To find the number of lead shots dropped, first we should find the volume of the cone, then the volume of the water flown out and the volume of each lead shot. Using these values, we shall calculate the number of lead shots dropped.

Solution :

• Finding the volume of the inverted cone :

Given,

• $\sf \pink{Height:8cm}$
• $\sf \pink{Radius:5cm}$

${\pmb{\sf{Volume_{(cone)}:\dfrac{1}{3}\pi r^2h}}}$

$\sf :\implies Volume_{(cone)}:\bigg(\dfrac{1}{3}\bigg)\bigg (\dfrac{22}{7}\bigg)(5cm)^2(8cm)$

$\green{\sf Volume_{(cone)}:\dfrac{4400}{21}cm^3}$

• Finding the volume of water flown out :

According to the question :

${\pmb{\sf{Volume~ of~ water~ flown~ out:\dfrac{1}{4}(Volume_{(cone)})}}}$

$\sf Volume~ of ~ water~ flown~out : \dfrac{1}{4}\bigg(\dfrac{4400}{21}\bigg)cm^3$

$\sf : \implies Volume \: of \: water \: flown \: out : \dfrac{1}{ \cancel4} \bigg( \dfrac{ \cancel{4400}}{21} \bigg) {cm}^{3}$

${ \sf{\purple{ Volume \: of \: water \: flown \: out : \dfrac{1100}{21} {cm}^{3} }}}$

• Finding the volume of each shot :

Given,

• $\sf \blue{Radius:0.5cm}$

${\pmb{\sf{Volume_{(sphere)}:\dfrac{4}{3}\pi r^3}}}$

$:\implies \sf Volume_{(sphere)}:\bigg(\dfrac{4}{3}\bigg)\bigg(\dfrac{22}{7}\bigg)(0.5cm)^3$

$:\implies \sf Volume_{(sphere)}:\bigg(\dfrac{88}{21}\bigg)(0.125)$

$\orange{ \sf Volume_{(sphere)}:\dfrac{11}{21}cm^3}$

• Finding the number of lead shots :

We know that :

${\pmb{\sf{No.~ of~ lead~ shots:\dfrac{Volume~ of~ water~ flown~ out}{Volume~of ~ each~lead~ shot}}}}$

$:\implies \sf No.~ of ~ lead~ shots:\dfrac{\frac{1100}{21}}{\frac{11}{21}}$

$:\implies \sf No.~ of~ lead~ shots :\dfrac{1100}{21}\bigg(\dfrac{21}{11}\bigg)$

$:\implies \sf No ~ of~lead~ shots:\dfrac{\cancel{1100}}{\cancel{21}}\bigg (\dfrac{\cancel{21}}{\cancel{11}}\bigg)$

${\red{\sf{No.~ of~lead~ shots:100}}}$

______________________

Therefore, the number of lead shots dropped are 100.

Answer 2

Answer:

Hlo

Fine wt about u

Very good afternoon