VOLUME OF SPHERES

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In addition to 3, student will be able to go above and beyond by applying what they know about volume of cones, spheres and cylinders.     

The student will know and use the formulas for volume of cones, cylinders and spheres. - Students can apply these formulas to solve real-world mathematical problems. 

With no help the student has a partial understanding of volume of cones, cylinders and spheres.

With help, the student may have a partial understanding of volume of cones, cylinders and spheres.

Even with help, the student is unable to find the volume of cones, cylinders and spheres.

Focus 12 - Learning Goal: The student will know and use the formulas for volume of cones, cylinders and spheres.

Sphere

V = 4/3(π r3)

To calculate the volume of a sphere.1. Cube the radius2.Multiply by 43.Divide by 34.Leave answers in

terms of π.

Find the volume of the sphere.

V = 4/3 (π r3)

V = 4/3 (π) (23)V = 4/3 (π) (8) V = 32/3 (π) V = 102/3

π ft3

Find the volume of the sphere.

V = 4/3 (π r3)

V = 4/3 (π) (73)V = 4/3 (π) (343) V = 1372/3 (π) V = 4571/3

π meters3

Find the radius.r = 7 m

Find the volume of the hemisphere.

A hemisphere is half of a sphere.

To find the volume of a hemisphere you could fine the volume of the sphere and divide by two which is the same as using the formula: V = 2/3(π r3)

V = 2/3 (π) (153)V = 2/3 (π) (3,375) V = 6,750/3 (π) V = 2,250 π in3

Work the problem backwards:

The volume of a sphere is 972π in3.

What is the radius of the sphere?

• Since we are missing the radius, work the problem backward.

• V = 4/3 π r3

• 972π = 4/3π • r3

• 729π = πr3

• π π• 729 = r3

• 9 = r

Multiply both sides by the reciprocal of 4/3. This would be 3/4.Divide by π.Cube root both sides.The radius of the sphere is 9 in.