A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm. What is the curved surface area (in cm2) of the cylinder? (Use π = )
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 924.
A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm.
The volume of a cone = 1/3πr2h
The volume of a cylinder = πr2h
The volume of a sphere = 4/3πr3
The curved surface area of a cylinder = 2πrh (Here, r = radius, h = height)
The volume of the cone = 1/3π × 72 × 7 = 1/3π × 73
The volume of each sphere = 4/3π × 73
Let the height of the formed cylinder be H
According to the question -
⇒ 1/3π × 73 + 2 × 4/3π × 73 = π × 72 × H
⇒ 73π(1/3 + 8/3) = π × 72 × H
⇒ 7 × (9/3) = H
⇒ 7 × 3 = H
⇒ 21 = H
So, the height of the formed cylinder is 21 cm
The curved surface area of the cylinder
⇒ 2 × 22/7 × 7 × 21 = 924 cm2