Volume of Pyramids, Cones & Spheres Return to table of contents

Given the same diameter and height for each figure, drag them to arrange in order of smallest to largest volume. How many filled cones do you think it would take to fill the cylinder? How many filled spheres do you think it would take to fill the cylinder?

Demonstration comparing volume of Cones & Spheres with volume of Cylinders click to go to web site

Volume of a Cone (Area of Base x Height)  3 (Area of Base x Height) 1 click to reveal A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h). (Area of Base x Height)  3 (Area of Base x Height) 1 3

Volume of a Sphere click to reveal V = 2/3 (Volume of Cylinder) r2 h) A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h). V = 2/3 (Volume of Cylinder) r2 h) 2/3 ( V = or V = 4/3  r3

(Just Ice Cream within Cone. Not on Top) How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? (Just Ice Cream within Cone. Not on Top) Answer: 3.14 x 9 28.26 (Area of Base) x 10 (Height) 282.6 3 (cone) = 94.2 in3

23 Find the volume. 9 in 4 in Answer: 150.72 V = (1/3)Bh V = 150.72 in3

24 Find the Volume 5 cm 8 cm Answer: 209.33 V = (1/3)Bh V = 209.33 cm3

If the radius of a sphere is 5.5 cm, what is its volume?

What is the volume of a sphere with a radius of 8 ft? 25 What is the volume of a sphere with a radius of 8 ft? Answer: 2143.57 V = (4/3) r 3 V = (4/3) (3.14)(8)3 V = 2143.57 ft 3

What is the volume of a sphere with a diameter of 4.25 in? 26 What is the volume of a sphere with a diameter of 4.25 in? Answer: 40.17 V = (4/3) r 3 V = (4/3) (3.14)(4.25/2)3 V = (4/3) (3.14)(2.125)3 V = 40.17 in3

Volume of a Pyramid (Area of Base x Height) click to reveal (Area of Base x Height)  3 (Area of Base x Height) 1 3 A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

Pyramids are named by the shape of their base.. The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h). V = Bh 1 3 1 3 V = Bh =5 m side length = 4 m

27 Find the Volume of a triangular pyramid with base edges of 8 in, base height of 4 in and a pyramid height of 10 in. 8 in 10 in 4 in Answer: 53.33 V = (1/3)Bh V = (1/3)[(1/2)(4(8))](10) V = (1/3)(16)(10) V = (1/3)(160) V  53.33 in3

28 Find the volume. 15.3 cm 7 cm 8 cm Answer: 285.6 V = (1/3)Bh V  285.6 in3