04/20/23 7.6: Surface Area and Volume of Spheres

7.6: Surface Area and Volume of a Sphere

Expectation:G1.8.1: Solve multistep problems involving

surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

What will we learn today?

04/20/23 7.6: Surface Area and Volume of Spheres

04/20/23 7.6: Surface Area and Volume of Spheres

Sphere

Defn: A sphere is the set of all points in space at a certain distance (_________) from a certain point (__________).

04/20/23 7.6: Surface Area and Volume of Spheres

Volume of a Sphere

Let V be the volume of a sphere with radius r.

Then V= ____________.

04/20/23 7.6: Surface Area and Volume of Spheres

A scoop of ice cream is 2 inches in diameter. An ice cream cone is 2 inches in diameter and has a height of 3.5 inches. If the ice cream melted before any of it was eaten, would it all fit in the cone?

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a Sphere

If the sphere were filled with pyramids, then the sum of the volumes of the pyramids would be the volume of the sphere.

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a Sphere

The volume of each pyramid is

⅓Bhpyr = ⅓Br.

Let’s assume there are n pyramids in the sphere.

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a Sphere

So the volume of the sphere is

1/3B1r + 1/3B2r + …+ 1/3Bnr

=1/3r(B1+B2+…+Bn).

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a SphereThe sum of the pyramids’ base areas is

the surface area of the sphere. So Vsphere= 4/3πr3 = ⅓Sr, where S is the surface area of the sphere.

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a SphereSolve the equation below to derive the formula for

the surface area of a sphere.

Vsphere= 4/3πr3 = ⅓Sr

04/20/23 7.6: Surface Area and Volume of Spheres

Surface Area of a Sphere

Let S be the surface area of a sphere with radius r. Then S =

04/20/23 7.6: Surface Area and Volume of Spheres

A child’s ball is 12 inches in diameter. Ignoring thickness, how much material was needed to make the ball?

A clay sphere has volume 36π cm3. If someone cuts straight through the sphere, the cross section is a circle. What is the area of the largest circular cross section?

A. 48 π cm2

B. 36 π cm2

C. 9 π cm2

D. 6 π cm2

E. 4 π cm2

04/20/23 7.6: Surface Area and Volume of Spheres

04/20/23 7.6: Surface Area and Volume of Spheres

Assignment pages 474-475,

#10-30 (multiples of 5), 32, 33, 37-42 (all).