How do you think through and answer a real world problem involving cones?

  For example: A conical glass flower vase has a base that is 6 inches in diameter and the vase holds approximately 113 cubic inches of water. What

is the height of the vase?

In this lesson you will learn how to solve real world problems by finding the

volume of cones.

Let’s ReviewLet’s Review

B= r2

h

Volume of ConeV = r2h

Let’s ReviewLet’s Review250 cubic inches of

water means I have a volume of 250 in3

inin2

in3

lengthareavolume

Let’s ReviewCore Lesson

V = r2h

A conical glass flower vase has a base that is 6 inches in diameter and the vase holds approximately 113 cubic inches of water. What

is the height of the vase?

Let’s ReviewCore Lesson

V = r2h Given: radius = 3 in volume = 113

in3

Find: height = ???

d=6 in so r=3

in

Let’s ReviewCore LessonV =r2h

113 in3 = 2 xh113 in3 = 32 xh

h = height 12 in

Let’s ReviewA Common MistakeV = r2h

V = 2 x 25.13 in3

= 2 x 25.13 in3

105 in5

Actual: h = 6 in

r= 2in

V = 25.13 in3

In this lesson you learned how to solve real world problems by

finding the volume of cones.

Let’s ReviewGuided Practice

A wax candle is in the shape of a right circular cone. The height of the candle

is 9cm and the candle contains approximately 167.55 cm3 of wax. What is the radius of the candle?

Let’s ReviewGuided PracticeV = r2h

113.1 cm3 = 2 x9cm2 = r =

= 2 cm

Find: radius= ?? Given: height = 9 cm

volume = 113.1 cm3

Let’s ReviewGuided Practice

A cement truck dumps 37.7 cubic feet of cement mix at a construction site in the shape of a conical mound. The base of the pile of cement has an approximate diameter of 6 ft. How tall is the mound of cement? 

Let’s ReviewGuided PracticeV = r2h

37.7 ft3 = 2 xh h =

h = 4 ft

Find: height = ?? Given: diameter = 6 ft

volume = 37.7 ft3

Let’s ReviewExtension Activities

An ice cream shop stores ice cream in cylindrical containers that are 25 cm tall with radius 15 cm. They sell scoops of ice cream that are 6 cm in diameter. Approximately how many scoops of ice cream will the store be able to serve out of one full cylindrical container?

Let’s ReviewQuick Quiz

1. An ice cream cone has a radius of 2 in. How much melted ice cream will the cone hold if it has a height of 6 inches?

2. An art sculpture has a base in the shape of a cone. It took approximately 2.1 cubic ft of cement to make the base which has a diameter of 2 ft. How tall is the base?