Volume & Surface Area of Solids

Objective: find the volume & surface area of cylinders, prisms, cones, pyramids and spheres

How are volume formulas related to area formulas?

Solid of Revolution: A 3-D figure “swept out” by rotating a

2-D figure around an axis

Ex 1) Name the solid that would be created

Ex 2) Name the solid that would be created

Ex 3) Name the solid that would be created

Ex 4) Name the solid that would be created

Volume Number of units it takes to fill the object

Number of units it takes to cover the outside of the object

Surface Area not including the “top” and “bottom”

Surface Area

Lateral Area

Volume, Surface Area, or Lateral Area?

The amount of water a cylindrical glass can hold

The amount of wrapping paper to wrap a box

The amount of water needed to fill a fish tank

The amount of paper wrapped around a soup can

The amount of cardboard used to make a paper towel holder

Volume = (Area of Base)(Height)

1. Type of solid: ____________________

Height of solid: _________________

Shape of base: _________________

Area of base:

V SA

2. Type of solid: ___________________

Height of solid: _________________

Slant height:______________

Shape of base: _________________

Area of base:

V SA

3. Type of solid: ____________________

Height of solid: _________________

Shape of base: _________________

Area of base:

Area of each face: V SA

4. Type of solid: ____________________

Height of solid: _________________

Shape of base: _________________

Area of base:

Perimeter of base:__________________

Slant height: V SA

5. Type of solid: _________________

V

SA

6. Type of solid: _______________________

Height of solid: _________________

Shape of base: _________________

Area of base:

V

1. A circle has a radius of 15 cm. What is the volume of the sphere made by rotating this circle?

2. A rectangle has a length of 3 m and a height of 5 m. What is the volume of the cylinder made by rotating this rectangle?

3. An isosceles triangle has base of 20 ft and an altitude of 30 ft. What is the volume of the cone made by rotating this triangle?

1. Given a sphere with a radius of 200 cm3, find the area of the perpendicular cross section right through its center

2. Given a cylinder with radius 7 in and height 10 in, find the area of a cross section that is parallel to its base

3. Given a cone with a radius of 6 ft and a height of 12 ft, find the area of the triangle formed by a perpendicular cross section down through the cone’s center