   Chapter 9.4, Problem 38E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# An ice cream cone is filled with ice cream as shown. What is the volume of the ice cream? Use your calculator. To determine

To find:

The volume of the ice cream in a cone.

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.

Half of a sphere is called a hemisphere.

Volume of hemisphere V=23πr3.

The surface area of a hemisphere S=2πr2.

A cone is a three dimensional solid figure formed by joining all the points from its circular base to a fixed point lying in a plane different from its base. The fixed point is called the vertex of the cone. The line segment which joins the vertex to the center of its base is called the axis of the cone. A right circular cone is formed when the axis is perpendicular to the base. An oblique circular cone is formed when the axis is not perpendicular to the base. An altitude of a cone is the perpendicular line drawn from the vertex to the plane of the base. In a right circular cone the length of the axis and the length of the altitude are the same. For a right circular cone, any line that joins the vertex to a point on the circular base is called slant height.

For right circular cone of base radius (r), slant height (l) and altitude (h),

Total surface area of the cone =πrl+r.

Curved or lateral surface area of the cone =πrl.

Volume of the cone =13πr2h.

Calculation:

Consider a cone with altitude (h)=3in

The altitude of cone with hemispherical cap (H)=4 in

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