Unit 6: Geometry

Lesson 7: Volume and Surface Area

Learning Goal

I can determine the volume for various prisms, pyramids, cylinders, cones, and spheres

Unit 6: Geometry

Prism: A three dimensional solid with two polygon shaped faces that are parallel and identical. The remaining sides are rectangular.

V = area of base X height

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Cylinder: A three dimensional solid with two circular faces that are parallel and identical.

V = area of base X height OrV =

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Pyramid:A pyramid is a 3D solid that has a polygon base and no top. The sides are triangular and meet at a point.

It takes the volume of three pyramids to make a prism with the same base and height.

SO…

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Pyramid:A pyramid is a 3D solid that has a polygon base and no top. The sides are triangular and meet at a point.

V = the volume of a prism with the same measurementsORV = ORV =

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Cone: A cone is a 3D solid that has a circular base and ends in a tip.

V = the volume of a cylinder with the same dimensions

V = X area of base X height(not side length)ORV =

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Sphere: A sphere is a 3D solid that has every point on its surface a distance of r away from its center. (Looks like a ball!)

V = the volume of a cylinder with the same radius and heightORV = ORV =

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Example 1: Find the volume

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Example 2: Find the volume

Lesson 7: Volume and Surface Area

Unit 6: Geometry

What is Surface Area? Surface area is the total area of the faces and curved surfaces of a solid figure.

Lesson 7: Volume and Surface Area

Unit 6: Geometry

PrismSA = 2(area of base) + (perimeter of base X height)

Lesson 7: Volume and Surface Area

Unit 6: Geometry

CylinderSA = 2(area of base) + (circumference of base X height)

SA = 2

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Square Based PyramidSA = (area of base) + 4(area of a triangle)

SA = (base squared) + 4(X height)

SA = b2 + 2bs

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Cone

SA = (area of base) + (half the perimeter of base X slant height)

SA = r = radiuss = slant height

(s)

Lesson 7: Volume and Surface Area

Unit 6: Geometry

SphereSA = 4

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Example 3: Find the Surface Area

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Example 4: Find the Surface Area of a sphere with a diameter of 12cm.

Lesson 7: Volume and Surface Area

Unit 6: Geometry

Practice

Page 413 Q# 2, 3ab, 6, 9 Page 421 Q# 2ad, 8, 9, 13 Page 427 Q# 1c, 2, 10, 14 Page 433 Q# 2ac, 6, 10

Page 439 Q# 10a, 11d, 5, 7 Page 445 Q# 1a, 2c, 3ab, 4, 11

Lesson 7: Volume and Surface Area