# Chapter 10

### Sam P

## All formulas in Chapter 10

Area of trapezoid: A=1/2(b1+b2)h

Area of circle: A=πr²

Surface area of a prism: S=2B+Ph

Surface area of a cylinder: S=2B+Ch

Lateral area of a cylinder: S=2πrh

Surface area of a pyramid: S=B+1/2*Pl

Surface area of a cone: S=πr²+πrl

Lateral area of a cone: S=πrl

Surface area of a sphere: S=4πr²

Volume of a prism: V=Bh

Volume of a cylinder: V=Bh

Volume of a pyramid: V=1/3*Bh

Volume of a cone: V=1/3*Bh

Volume of a sphere: V=4/3πr³

## 10.1

## Area of parallelograms and trapezoids

Vocabulary

~Base of a parallelogram- The length of any one of a parallelogram's sides..

~Height of a parallelogram- The perpendicular distance between the base and the opposite side.

~Bases of a trapezoid- The two parallel sides.

~Height of a trapezoid- The perpendicular distance the two bases.

**Formulas:**

Parallelogram: A=bh

Trapezoid: A=(b1+b2)h

**b1= base one, b2= base two, h= height**

## Practice problems

## 10.2

## Area of circles

Vocabulary

~Area- The amount of surface the figure covers.

~Circle- The set of all points in a plane that are the same distance from a fixed point called the center.

~Radius- The distance from the center to any point on the circle.

~Diameter- The distance across the circle through the center, or twice the radius.

~Circumference- The distance around the circle.

~Pi- A non- terminating decimal that with any circle it is the circumference divided by its diameter.

**Formulas:**

A=πr²

**A= Area, r= radius**

## Practice problems (use 3.14 for pi and round to nearest hundreth)

## 10.3

~Solid- A three-dimensional figure that encloses a part of space.

~Polyhedron- A solid that is encloses by polygons.

~Faces- The polygons that form a polyhedron.

~Prism- A polyhedron with two congruent bases that lie in parallel planes. The other faces are rectangles.

~Pyramid- A polyhedron with one base. The other faces are triangles.

~Cylinder- A solid with two congruent circular bases that lie in parallel planes.

~Cone- A solid with one circular base.

~Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center.

~Edge- Where faces of a polyhedron meet.

~Vertex- A point where three or more edges meet.

## Practice problems- Classify the solid then tell whether it is a polyhedron

## 10.4

## Surface area of prisms and cylinders

Vocabulary

~Net- A two-dimensional pattern that when folded forms a solid.

~Surface area- The sum of the areas of a polyhedrons faces.

~Lateral surface area- The surface area of a three-dimensional figure excluding the area of its bases.

**Formulas:**

Prism: S=2B+Ph

Cylinder: S=2B+Ch

S=2πr²+2πrh

lateral area of cylinder: 2πrh

**S=Surface area, B= Area of the objects base, P= Perimeter of the base, h=height**

## Practice problems- Find the surface area of the solid

## 10.5

## Surface area of pyramids and cones

Vocabulary

~Slant height- The height of a lateral face, which is any face that is not a base.

**Formulas:**

Pyramid: S=B+1/2*Pl

Cone: S=πr²+πrl

Lateral surface area of a cone: S=πrl

**S= Surface area, B= Area of the objects base, P= perimeter of the base, l= slant height**

**r= radius, l= slant height**

## Practice problems

## 10.6

## Volume of prisms and cylinders

Vocabulary

~Volume- A measure of the amount of space it occupies.

**Formulas:**

Prism: V=Bh

Cylinder: V=Bh

V=πr²*h

**V= Volume, B= Area of base, h= height**

## Practice problems- Find the volume of the solids

## Real life example

## 10.7

## Volume of pyramids and cones

Vocabulary

~Pyramid- A polyhedron with one base. The other faces are triangles.

~Cone- A solid with one circular base.

~Volume- A measure of the amount of space it occupies.

**Formulas:**

Pyramid: V=1/3*Bh

Cone: V=1/3*Bh

V=1/3*πr²*h

**V= Volume, h= height**

## Practice problems- Find the volume of the solids

## Sphere

## Surface area and volume of spheres

Vocabulary

~Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center.

~Volume- A measure of the amount of space it occupies.

**Formulas:**

S=4πr²

V=4/3*πr³

**S=Surface area, r= radius**

**V= Volume, r= radius**

## Practice problems

## #1 find the volume Answer= 523.3cm³ | ## #2 find the surface area Answer= 1256cm² | ## #3 find the volumeV=4/3*πr³ V=4/3*3.14*14³ V=4/3*3.14*2744 V=4/3*8616.16 V=11488.2cm³ |