a cone and a cylinder have equal radii,r, and equal altitudes, h. If the slant height is l, then what is the ratio of the lateral area of the cone to the cylinder?

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07-04-2021
Mathematics

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a cone and a cylinder have equal radii,r, and equal altitudes, h. If the slant height is l, then what is the ratio of the lateral area of the cone to the cylinder?

Sagot :

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 1 · 2022-08-12T05:20:46-04:00

The ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.

What are a cone and a cylinder?

The solid formed by two congruent closed curves in parallel planes along with the surface created by line segments connecting the corresponding points of the two curves is known as a cylinder.

A cylinder with a circular base is known as a circular cylinder. Based on the form of its base, a cone is given a name.

It is given that a cone and a cylinder have equal radii,r, and equal altitudes, h. The ratio of the lateral surface area of the cone to the cylinder will be calculated as below:-

The lateral area of the cone = πr√(h²+r²)

The lateral area of the cylinder = 2πrh

The ratio will be calculated as:-

R = πr√(h²+r²) / 2πrh

R = √(h²+r²) / 2h

Therefore, the ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.

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What are a cone and a cylinder?

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