Question

A solid cone of lead with radius 2 cm and height 6 cm is melted and cast into
a right circular cylinder of height 2 cm. Find the radius of the base of the cylinder.​

Answer 1

Answer:

80π cm2

Step-by-step explanation:

For cylinder, radius (r1) = 8 cm, height (h1) = 2 cm For cone, radius (r2) = ?, height (h2) = 6 cm Now, Volume of cone = Volume of cylinder

⇒ 13πr22h2=πr21h113πr22h2=πr12h1

⇒ 13πr22×6=π×8×8×213πr22×6=π×8×8×2

⇒ r22=π×8×8×2×3π×6=64r22=π×8×8×2×3π×6=64 ⇒ r2 = 8 cm

Curved surface of cone = πr2l

= πr2h22+r22−−√πr2h22+r22

= π x 8 x 36×64

−√=(π×8×10)36×64

=(π×8×10)cm2

= 80π cm2.

Answer 2

Answer:

Step-by-step explanation:

(b) 80π cm2

For cylinder,

radius (r1) = 8 cm,

height (h1) = 2 cm  

For cone,

radius (r2) = ?,

height (h2) = 6 cm  

Now, Volume of cone =

Volume of cylinder ⇒ 13πr22h2=πr21h113πr22h2=πr12h1 ⇒ 13πr22×6=​​π×8×8×213πr22×6=​​π×8×8×2 ⇒ r22=π×8×8×2×3π×6=64r22=π×8×8×2×3π×6=64 ⇒ r2 = 8 cm Curved surface of cone = πr2l = πr2h22+r22−−−−−−√πr2h22+r22 = π x 8 x 36×64−−−−−−√=(π×8×10)36×64=(π×8×10)cm2 = 80π cm2.