Question

a corn shaped like a cone has a base radius 7cm and height 24cm. if each 1cm² of the surface carries an average 4 grains. find how many grains you would find on the entire corn (pie=22/7)​

Answer 1

Question :

a corn shaped like a cone has a base radius 7cm and height 24cm. if each 1cm² of the surface carries an average 4 grains. find how many grains you would find on the entire corn .

Answer :

$\sf\pink {Given :}$

• Radius of the base is 7 cm .

• Height is 24 cm .

• Each 1 cm Sq of the surface carries an average 4 grains .

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

• grains on the entire corn ?

Explanation :

To find the number of grains on the entire corn we need to find the total surface area of the corn and then divide it by the number of grains 1 Sq cm carries .

Total surface area = $\\ \sf{\pi r ( l + r )}$

• l = slanting height

l = $\sf {\sqrt{{r}^{2} + {h}^{2}}}$

l = $\sf {\sqrt{{7}^{2} + {24}^{2}}}$

l = $\sf {\sqrt{49 + 576}}$

l = $\sf {\sqrt{625}}$

l = $\sf {25}$

Total surface area = $\\ \sf{\dfrac {22}{7}\times 7\times ( 25 + 7)}$

$\\ \longrightarrow\sf{22\times ( 25 + 7 )}$

$\\ \longrightarrow\sf{22\times 32}$

$\\ \longrightarrow\sf{704}$

• Therefore the total surface area is 704 cm Sq.

Number of grains = $\sf {\dfrac {704}{4}}$

$\\ \longrightarrow\sf{176}$

• Therefore the total number of grains is 176 .