Volume of Spheres Volume of Spheres The volume
- Slides: 27
Volume of Spheres
Volume of Spheres The volume of a sphere is the number of unit cubes, or cubic units, needed to fill the sphere. You can find the formula for the volume of a sphere by comparing it with the volume of a cylinder with a height and diameter equal to the diameter of the sphere.
Volume of a Sphere The diameter of a cylinder and a sphere are the same.
Volume of a Sphere The height of the cylinder equals the diameter of the sphere, or 2 r
Volume of a Sphere So the cylinder has a height and diameter equal to the diameter of the sphere.
Volume of a Sphere Suppose you marked off a cylinder in thirds.
Volume of a Sphere Now fill the cylinder with water up to the 1/3 mark.
Volume of a Sphere If you drop the sphere inside the cylinder, the water inside the cylinder rises.
Volume of a Sphere When the sphere is completely submerged in the cylinder, the water level reaches the top of the cylinder.
Volume of a Sphere Use the formula V = πr²h to find the volume of the cylinder.
Volume of a Sphere In this cylinder, we said the height is equal to 2 r. So, V= πr²(2 r) or V= 2πr³.
Volume of a Sphere The formula for the volume of this particular cylinder is V = 2πr³
Volume of a Sphere Since the sphere filled up two-thirds of the space in the 2 (Volume of the cylinder) 3 cylinder, the Volume of the sphere must = Thus, the formula for the volume of this particular sphere is: V= 2 3 (2πr³)
Volume of a Sphere Simplified, the volume of a sphere equals V= 4 3 πr³
Volume of a Sphere To the nearest cubic foot, how much space is contained inside the water-walking ball? Use 3. 14 for π.
Volume of a Sphere Find the volume of the sphere to the nearest cubic inch. Use 3. 14 for π.
Volume of a Sphere To the nearest cubic inch, how much space is there inside the ball for the hamster? Use 3. 14 for π.
HW: Volume of Spheres
Example Problems: Find the volume of the sphere. Formula for Volume of a Sphere = 4/3 ( π r³) 4/3 (π (3)³) 4/3 (9π) 3 in. 4/3 (28. 26) 113. 04/3 V = 37. 68 in. ³
Example Problems: Find the volume of the sphere. Formula for Volume of a Sphere = 4/3 ( π r³) 4/3 (π (10)³) 4/3 (1000π) 10 in. 4/3 (3, 140) 12, 560/3 V = 4, 186 2 __ 3 in. ³
Volume of a Sphere When it spins, the quarter forms what appears to be a sphere. To the nearest hundredth of a cubic inch, how much space does the spinning quarter occupy. Use 3. 14 for �. . �== 4 3 � � 3 �== 4 3 (3. 14) (0. 4975 3 ) �==0. 52 �� 3 3
Volume of a Sphere To the nearest tenth of a cubic millimeter, what is the volume of the sphere that appears when a nickel is spinning. Use 3. 14 for �. . �== 4 3 � � 3 �== 4 3 (3. 14) (10. 605 3 ) �==4993. 4 �� 3 3
Volume of a Sphere An agate geode is spherical and has a volume of about 904 �� 3 3. Geodes are often found in gem shops sliced in half like the one shown. What is the radius of the geode to the nearest centimeter? Use 3. 14 for �. . �== 4 3 � � 3 904= 4 3 (3. 14) (� 3 ) �==6 ��
Volume of a Sphere A gazing ball in the center of a garden has a volume of 904. 3 �� 3 3. To the nearest centimeter, find the diameter of the gazing ball. Use 3. 14 for �. . �== 4 3 � � 3 904. 3= 4 3 (3. 14) (� 3 ) �==6 �� � �==12 ��
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