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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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A sphere is inscribed within a right circular cylinder whose altitude and diameter have equal measures.

a) Find the ratio of the surface area of the cylinder to that of the sphere.

b) Find the ratio of the volume of the cylinder to that of the sphere.

Chapter 9.4, Problem 25E, A sphere is inscribed within a right circular cylinder whose altitude and diameter have equal

To determine

To find:

The ratio of the surface area of the cylinder to that of the sphere.

Explanation

Approach:

A sphere is a three dimensional solid figure, which is made up of all the points in space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere.

The surface area of a sphere S =4πr2, where r is the radius of the sphere.

All solid bodies occupy space. The measure of occupied space is called the volume of the object.

Volume of a sphere V=43πr3.

A solid generated by the revolution of a rectangle about one of its sides is called a right circular cylinder.

A right circular cylinder has two plane ends. Each plane end is circular in shape, and the two plane ends are parallel; that is they lie in parallel planes. Each of the plane ends is called a base of the cylinder. The line segment joining the centers of the two bases is called the axis of the cylinder. The axis is always perpendicular to the bases of a right circular cylinder.

The radius of the circular bases is called the radius(r) of the cylinder.

The length of the axis of the cylinder is called the altitude (h) of the cylinder.

Total surface area of a cylinder=2πr(h+r).

Curved or lateral surface area of a cylinder=2πrh.

Volume of cylinder=πr2h.

Calculation:

Consider a sphere is inscribed within a right circular cylinder where,

Altitude (h) = Diameter (d) = 2 Radius (r).

Therefore h = 2r,

Total surface area of cylinder,

=2πr(h+r)

Putting value h = 2r,

=2πr(2r+r)

Total surface area of sphere=4πr2

To determine

To find:

The ratio of the volume of the cylinder to that of the sphere.

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