Math in Focus 7B - Chapter 8 - 8.1: Recognizing Cylinders, Cones, Spheres, and Solids; 8.2: Finding Volume and Surface Area of Cylinders

cone

A cone has a circular base, a curved surface, and one vertex.

plane

A flat surface that extends infinitely in two directions.

cylinder

A solid cylinder has a curved surface and two parallel bases that are congruent circles.

sphere

A sphere has a curved surface. Every point on the surface is an equal distance from the center of the sphere.

Surface area of a cylinder =

Area of bases + Area of the curved surface 2πr² + 2πrh

hemisphere

If you slice a sphere in half, you will get two hemispheres.

The cross section of a sphere is a

circle

lateral surface

The curved surface of a cone.

slant height

The distance from the vertex to any point on the circumference of the base.

surface area

The sum of the area of the faces and curved surfaces of a solid figure.

How do you find the volume of a cylinder given its radius and height?

V = Bh V = πr² × h

cross section

When a flat plane slices through a solid

If given the volume and radius, can you find the height of a cylinder?

Yes, V = πr² × h

If you are given the surface area and height of a cylinder, can you find the radius?

Yes, area of the curved surface is 2πrh. Substitute in what you know and solve for h.

If you know the diameter of a cylinder's base, can you find the radius?

Yes, divide by 2 because the radius is half of the diameter.

volume

a measure of space enclosed in a solid figure

volume of a cylinder

area of the base x height B × h πr² × h

How do you square a number?

multiply the number by itself Examples: 2² = 2 × 2 = 4 3² = 3 × 3 = 9 4² = 4 × 4 = 16

If you slice through a square pyramid so that the cross section is parallel to its base, the cross section is a

square

If you slice through a square pyramid so that the cross section is perpendicular to the base, the cross section is a

triangle