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Question

The volume and the total surface area of a cone whose height and slant height are 12 cm and 13 cm respectively are ________.


A
80π cm3 and 90π cm2
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B
100π cm3 and 90π cm2
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C
100π cm3 and 80π cm2
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D
85π cm3 and 95π cm2
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Solution

The correct option is B 100π cm3 and 90π cm2

Slant height of the cone is given by

l2=(h2+r2)
r=l2h2
r=132122
r=5 cm

So, volume of cone
=13π r2h
=13×π×52×12
=13×π ×25×12
=100π cm3

Now, total surface area
=(π×r× l)+(π×r2)
=π×5× 13+π×25
=90π cm2


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