Answer
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Hint:
It is given that r = 1.4 cm and h = 12 cm.
Now, using the formula $l = \sqrt {{r^2} + {h^2}}$, find l of the cone.
Thus, find the area of the cone by $A = \pi rl$.
Finally, $A \times 4$ will give the number of corn grains in the entire cob.
Complete step by step solution:
Here, it is given that the radius of its broadest end is 1.4 cm and length (height) as 12 cm of the surface of the cob.
Thus, r = 1.4 cm and \[h = 12\] cm.
So, we get l using the formula $l = \sqrt {{r^2} + {h^2}} $ .
$\therefore l = \sqrt {{{\left( {1.4} \right)}^2} + {{\left( {12} \right)}^2}} $
$
= \sqrt {1.96 + 144} \\
= \sqrt {145.96} \\
= 12.08
$
The C.S.A. of the cone is given by $A = \pi rl$ .
$
\therefore A = \pi \left( {1.4} \right)\left( {12.08} \right) \\
= \dfrac{{22}}{7}\left( {1.4} \right)\left( {12.08} \right) \\
= 53.15 \\
= 53.2c{m^2}
$
Thus, the area of the cone cob is $53.2c{m^2}$.
It is also given that, number of corn grains in the $1c{m^2}$ area is 4.
Thus, the number of corn grains carried in $53.2c{m^2}$ is $53.2 \times 4 = 212.8 = 213$ approximately.
So, option (C) is correct.
Note:
Here, the number 53.15 is rounded to 53.2 because the second digit after the decimal is 5, and if the digit after decimal is greater than or equal to 5 we add +1 to the previous digit i.e. 1 after the decimal.
Similarly, 212.8 is rounded off to 213, because the digit after decimal is greater than 5 i.e. 8, so we add +1 to 212 = 213.
It is given that r = 1.4 cm and h = 12 cm.
Now, using the formula $l = \sqrt {{r^2} + {h^2}}$, find l of the cone.
Thus, find the area of the cone by $A = \pi rl$.
Finally, $A \times 4$ will give the number of corn grains in the entire cob.
Complete step by step solution:
Here, it is given that the radius of its broadest end is 1.4 cm and length (height) as 12 cm of the surface of the cob.
Thus, r = 1.4 cm and \[h = 12\] cm.
So, we get l using the formula $l = \sqrt {{r^2} + {h^2}} $ .
$\therefore l = \sqrt {{{\left( {1.4} \right)}^2} + {{\left( {12} \right)}^2}} $
$
= \sqrt {1.96 + 144} \\
= \sqrt {145.96} \\
= 12.08
$
The C.S.A. of the cone is given by $A = \pi rl$ .
$
\therefore A = \pi \left( {1.4} \right)\left( {12.08} \right) \\
= \dfrac{{22}}{7}\left( {1.4} \right)\left( {12.08} \right) \\
= 53.15 \\
= 53.2c{m^2}
$
Thus, the area of the cone cob is $53.2c{m^2}$.
It is also given that, number of corn grains in the $1c{m^2}$ area is 4.
Thus, the number of corn grains carried in $53.2c{m^2}$ is $53.2 \times 4 = 212.8 = 213$ approximately.
So, option (C) is correct.
Note:
Here, the number 53.15 is rounded to 53.2 because the second digit after the decimal is 5, and if the digit after decimal is greater than or equal to 5 we add +1 to the previous digit i.e. 1 after the decimal.
Similarly, 212.8 is rounded off to 213, because the digit after decimal is greater than 5 i.e. 8, so we add +1 to 212 = 213.
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