Exercise If a pyramid and a cone have bases with the same area and altitudes that are equal, are their surface areas equal? no

If a pyramid and a cone have bases with the same area and altitudes that are equal, are their volumes equal? yes Exercise

In this text, what is the difference between h and H? h = length of the altitude of a plane figure and H = length of the altitude of a solid figure. Exercise

What would the calculation of bhH give? the volume of a triangular prism Exercise

h h w w l l h h w w l l

Formula: Volume of a Pyramid or a Cone V = BHThe volume of a pyramid or cone (V) is equal to one- third the area of the base (B) times the height (H)

Find the volume of the square pyramid. = 256 cm 3 V = BH = (8 2 )(12) cm 12 cm Example 1

Find the volume of the cone. ≈ cm 3 V = BH =  (4 2 )(6) = 32  = 32(3.14) 6 cm 4 cm Example 2

What is the volume of a pyramid if its height is 10 units and its base is 8 units by 12 units? 320 units 3 Example

What would happen to the volume of the pyramid in the previous question if its length were doubled? The volume would be doubled. Example

What would happen to the volume if any single dimension were doubled? Example The volume would be doubled.

What would happen if all the dimensions were doubled? The volume would be multiplied by a factor of 2 3 = 8. Example

What is the volume of a square pyramid if each side of its base is 6 units and its height is 5 units? 60 units 3 Example

What would happen to the volume of the pyramid in the previous question if the sides of the square base were doubled? The volume would be multiplied by a factor of 2 2 = 4. Example

Formula: Volume of a Sphere V =  r 3 The volume of a sphere (V) is equal to the product of, , and the radius cubed (r)

Find the volume of a sphere with a diameter of 15 ft. to the nearest hundredth. Find the number of gallons it will hold. (1 ft. 3 = 7.48 gal.) r = = 7.5 ft Example 3

V =  r =  (7.5 3 ) =  ( ) =  1, ≈ 1, ft. 3 Example 3

≈ 13,212 gal. 7.48(1,766.25) Example 3

Find the radius of a sphere with a volume of 288  m 3. V =  r  r 3 = 288   r 3 = (288  ) ( ) Example 4

 r 3 = 216  r 3 = 216 r = 6 m Example 4

What is the volume of a sphere with a radius of 6 units? Example units 3

A city needs a 10,000 m 3 water tower for its increasing population. What should the radius be if the water tower is in the form of a sphere? Example m

A grain storage bin is a steel cylinder with a conical top. One company markets a bin that is 18’ in diameter, 16’ high at the eaves, and 21’ high at the peak. Exercise

What is the maximum number of bushels of wheat (rounded to the nearest bushel) that can be stored in the bin? There are 0.8 bushels in one cubic foot. Exercise

V =  r 2 H +  r 2 H = 1,296   = 1,431  ft. 3 =  (9 2 )(16) +  (9 2 )(5) = 1,431  ft bu. 1 ft. 3 ( ) ≈ 3,595 bu. Exercise