Question:A cone and a cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is 3m, then the slant height of the cone (in m) is
Answer:
Given the radius of cylinder and cone are the same because there base areas are same.
Curved surface of cylinder = curved surface area of the cone
∴2πrh=πrl
∴l=2h
Given, height of cylinder =3 cm
Therefore, slant height of cone =6 cm
The volume of the cone is 22π.
Volume of a cylinder = πr²h
55π = πr²(5)
55π = 5πr²
r² = 55π/5π
r² = ✓11
r = 3.3
The volume of the cone will be:
= 1/3πr²h
= 1/3 × π × 3.3² × 6
= 1/3 × 11 × 6 × π
= 22π
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