Question

A corn Cob like a cone has the radius of its broadest end as 3.5 cm and length 21 cm. If each 1 cm ^2 of the surface of the cob carries 5 granes , Find how many granes the cob contains.​

Answer 1

Answer:

Answer

CSA of cone cob = πrl

r=2.1cm,h=20cm

Now, l=

r

2

+h

2

=

(2.1)

2

+(20)

2

l=

404.41

=20.11cm

∴ CSA of corn cab =

7

22

×2.1×20.11=132.73cm

2

Number of grains on 1 cm

2

of the surface corn cob =4

∴ Number of grain on 132.73 cm

2

of the surface of corn cab =132.73×4≈531

Answer 2

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$\bf \scriptsize{Radius = 3.5 cm \: And \: Height = 21 cm}$

$\bf \scriptsize{Radius = 3.5 cm \: And \: Height = 21 cm}$$\bf \scriptsize \: Slant height ( l ) = h ^{2} + r^{2} = (21)^{2} + (3.5)^{2} \\ \bf \scriptsize{ ⇛441 + 12.25 = 453.25 } \\ \bf \scriptsize{l = \sqrt{453.25} } \\ \bf \scriptsize l = 21.29 \: cm.$

$\bf \scriptsize{Radius = 3.5 cm \: And \: Height = 21 cm}$$\bf \scriptsize \: Slant height ( l ) = h ^{2} + r^{2} = (21)^{2} + (3.5)^{2} \\ \bf \scriptsize{ ⇛441 + 12.25 = 453.25 } \\ \bf \scriptsize{l = \sqrt{453.25} } \\ \bf \scriptsize l = 21.29 \: cm.$$\bf \scriptsize{Therefore , \: The \: curved \: Surface \: area \: of \: the \: Cob \: } \\ \bf \scriptsize{⇛\pi \: r \: l = \frac{22}{7} \times 3.5 \times 21.29} \\ \bf \scriptsize{⇛ 22 \times 0.5 \times 21.29} \\ \bf \scriptsize{⇛234.19 \: cm^{2} }$

$\bf \scriptsize{Radius = 3.5 cm \: And \: Height = 21 cm}$$\bf \scriptsize \: Slant height ( l ) = h ^{2} + r^{2} = (21)^{2} + (3.5)^{2} \\ \bf \scriptsize{ ⇛441 + 12.25 = 453.25 } \\ \bf \scriptsize{l = \sqrt{453.25} } \\ \bf \scriptsize l = 21.29 \: cm.$$\bf \scriptsize{Therefore , \: The \: curved \: Surface \: area \: of \: the \: Cob \: } \\ \bf \scriptsize{⇛\pi \: r \: l = \frac{22}{7} \times 3.5 \times 21.29} \\ \bf \scriptsize{⇛ 22 \times 0.5 \times 21.29} \\ \bf \scriptsize{⇛234.19 \: cm^{2} }$$\bf \scriptsize{Number \: of \: granes \: of \: corn \: on \: 1 cm ^{2} = 5}$

$\bf \scriptsize{Radius = 3.5 cm \: And \: Height = 21 cm}$$\bf \scriptsize \: Slant height ( l ) = h ^{2} + r^{2} = (21)^{2} + (3.5)^{2} \\ \bf \scriptsize{ ⇛441 + 12.25 = 453.25 } \\ \bf \scriptsize{l = \sqrt{453.25} } \\ \bf \scriptsize l = 21.29 \: cm.$$\bf \scriptsize{Therefore , \: The \: curved \: Surface \: area \: of \: the \: Cob \: } \\ \bf \scriptsize{⇛\pi \: r \: l = \frac{22}{7} \times 3.5 \times 21.29} \\ \bf \scriptsize{⇛ 22 \times 0.5 \times 21.29} \\ \bf \scriptsize{⇛234.19 \: cm^{2} }$$\bf \scriptsize{Number \: of \: granes \: of \: corn \: on \: 1 cm ^{2} = 5}$$\bf \scriptsize{Therefore , \: The \: number \: of \: granes \: on \: the \: entire \: Curved \: surface \: of \: corn \: cob = \: 234.19 \times 5} \\ \bf \scriptsize{ = 1171 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

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