Find the volume of a sphere

Slides:

Advertisements

Similar presentations

EXAMPLE 3 Find the height of a cylinder COMPACT DISCS

Advertisements

EXAMPLE 3 COMPACT DISCS You are wrapping a stack of 20 compact discs using a shrink wrap. Each disc is cylindrical with height 1.2 millimeters and radius.

Introduction There are many applications for solid geometry in the real world. In this lesson, you will apply the formulas for the volumes of solids to.

12.6.  Sphere – Set of all point in space equidistant from a given point.  Center  Radius – a segment from the center to a point on the sphere.  Chord.

Using Radius to Find Circumference

How do I find the surface area and volume of a sphere?

MM2G4 Students will use apply surface area and volume of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect.

EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS

EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. =

Calculating the volume of a solid Sphere, cone and pyramid.

EXAMPLE 3 Finding the Volume of a Cone Native Americans Many Native American tribes built tepees that were similar to a cone in shape. A tepee has a height.

Standardized Test Practice

Find the area of each circle.

 1.) Total surface area?  2.) 3 in a row removed?  3.) Other 3 removed?

Volume of Prisms Volume of Cylinders Volume of Cones Volume of Spheres Potpourri

Surface Area of Prisms and Cylinders

Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches. Round to the nearest tenth. Find the.

EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.

11-5 Volumes of Pyramids and Cones. Volume of a Pyramid The volume of a pyramid is one third the product of the area of the base and the height of the.

Chapter 13 Volume.

x x 3 ft 36 in 24 yd = 72 ft 5 yd = 180 in 1 yd 1 yd

11. 7 Volume of Pyramids and Cones 11

Surface Area and Volume of Cones

EXAMPLE 1 Find the volume of a solid Find the volume of the solid. V = Bh 1 3 = 36 m 3 a.a. = ( 4 6)(9)

Chapter 1 Measurement. §1.1 Imperial Measures of Length.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.5.

VOLUME OF SOLIDS. VOLUME OF PRISMS V = Area of Base x Height V = 6 cm 8 cm 10 cm All measurements must be in the same UNIT before doing ANY calculations.

Volume of CYLINDERS V olume = Πr 2 h Volume is in: UNITS Gallon = 231 in 3 1 cubic foot of water equals gallons.

Finding Volumes of Prisms

Lesson 18 Surface Area & Volume Volume of Cylinders.

$200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 Radius & Diameter Volume.

Use the formula for circumference

Use trigonometry to find the volume of a cone

Use trigonometry to find the volume of a cone

10-7 Surface Areas and Volumes of Spheres Two Theorems.

Prisms & Pyramids 1 Prism and Pyramids Formulas Prisms: Lateral Area: L.A. = ph (p = perimeter, h = height) Surface Area: S.A. = ph + 2B (B = area of base)

Surface Area & Volume of Spheres Section Vocab Sphere - the set of all points in space equidistant from a given point called the center. Radius.

EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded.

Warm-Up Exercises 1. Regular hexagon, side length 9 in. 2. Circle, radius 15 m ANSWER in. 2 ANSWER m 2 Find the area of each polygon or circle.

EXAMPLE 3 Standardized Test Practice SOLUTION To find the slant height l of the right cone, use the Pythagorean Theorem. l 2 = h 2 + r 2 l 2 =

EXAMPLE 1 Drawing a Net Draw a net of the triangular prism. SOLUTION

Example 3 Multiplying Mixed Numbers POSTCARDS A designer creates postcards that are inches long and inches wide. Find the area of the postcard

Example 1 Find the Area of a Right Triangle Find the area of the right triangle. SOLUTION Use the formula for the area of a triangle. Substitute 10 for.

Surface Areas of Prisms and Cylinders

Volume of Pyramids and Cones

Find the surface area of a sphere

VOLUME of a CONE and UNKNOWN VALUES PRE389 When finding unknown values, plug what you know into the formula and solve for what’s missing! Find the height.

Volume of Cones & Spheres

EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.

Surface Area of Pyramids and Cones

Find the Area of a Square Example 1 Find the area of the square. SOLUTION Use the formula for the area of a square and substitute 9 for s. A = s 2 Formula.

Surface Areas and Volumes of Spheres LESSON 12–6.

Transparency 2 Click the mouse button or press the Space Bar to display the answers.

Volume of Pyramids and Cones Section 9.5. Objectives: Find the volumes of pyramids and cones.

Sec. 12.6: Surface Area and Volume of Spheres A sphere is the set of all points in space equidistant from a given point, called the center of the sphere.

Find the area of each circle.

Calculate Volume of Prisms & Cylinders

Find the area of each polygon or circle.

Volumes of Pyramids and Cones

Find the volume of the cone. Round to the nearest tenth if necessary.

EXAMPLE 1 Find the volume of a solid Find the volume of the solid. a.

Lesson 15.1 – Volumes of Cylinders

Find the surface area of a sphere

Find the volumes of cones, and spheres.

Find the surface area of a sphere

Volumes of Pyramids and Cones

11.8 Surface Area and Volume of Spheres

Objective: To find…. Find volumes of prisms and cylinders.

Goal: The learner will find surface area and volumes of spheres.

Five-Minute Check (over Lesson 11–2) Mathematical Practices Then/Now

Presentation transcript:

Find the volume of a sphere EXAMPLE 4 Find the volume of a sphere The soccer ball has a diameter of 9 inches. Find its volume. SOLUTION The diameter of the ball is 9 inches, so the radius is = 4.5 inches. 9 2 V = πr3 4 3 Formula for volume of a sphere = π(4.5)3 4 3 Substitute.

Find the volume of a sphere EXAMPLE 4 Find the volume of a sphere = 121.5π Simplify. ≈ 381.70 Use a calculator. The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. ANSWER

Find the volume of a composite solid EXAMPLE 5 Find the volume of a composite solid Find the volume of the composite solid. SOLUTION = πr2h – ( πr3) 1 2 4 3 Formulas for volume = π(2)2(2) – π(2)3 2 3 Substitute. 2 3 = 8π – (8π) Multiply.

Find the volume of a composite solid EXAMPLE 5 Find the volume of a composite solid = π – π 24 3 16 Rewrite fractions using least common denominator. 8 3 = π Simplify. The volume of the solid is π, or about 8.38 cubic inches. 8 3 ANSWER

GUIDED PRACTICE for Examples 4 and 5 4. The radius of a sphere is 5 yards. Find the volume of the sphere. Round your answer to two decimal places. The volume of the sphere is 523.81yd2 ANSWER

GUIDED PRACTICE for Examples 4 and 5 5. A solid consists of a hemisphere of radius 1 meter on top of a cone with the same radius and height 5 meters. Find the volume of the solid. Round your answer to two decimal places. The volume of the solid is 7.33m2 ANSWER