Question

a cone cob shaped somewhat like a cone,has the radius of its brodest end as 12 cm and length (height) as 20 cm.if each 1 cm^2 of c.s.a carries an average of 4 grams.find how many grains you would find on the entire con cob

Answer 1

since the grains of corn are found on the curved surface of the corn cob.

Total number of grains on the corn cob = Curved surface area of the corn cob x Number of grains of corn on 1cm^2

Now,
find the curved surface area of the corn cob.
r = 2.1 cm
h = 20 cm
Let l be the slant height of the corn cob. Then,
l^2 = r^2+ h^2
= (2.1)^2 + (20)^2
=4.41 + 400
=404.41
l =20.11

C.S.A. of cone= πrl
= 22/7 * 2.1 * 20.11
= 132.73 cm^2

We know that,
Total no. of grains on the corn cob
= 132.73 * 4
= 530.92

so, approximately there are 531 grains.

Answer 2

since the grains of corn are found on the curved surface of the corn cob.

Total number of grains on the corn cob = Curved surface area of the corn cob x Number of grains of corn on 1cm^2

Now,

find the curved surface area of the corn cob.

r = 2.1 cm

h = 20 cm

Let l be the slant height of the corn cob. Then,

l^2 = r^2+ h^2

= (2.1)^2 + (20)^2

=4.41 + 400

=404.41

l =20.11

C.S.A. of cone= πrl

= 22/7 * 2.1 * 20.11

= 132.73 cm^2

We know that,

Total no. of grains on the corn cob

= 132.73 * 4

= 530.92