Standardized Test Practice

Slides:

Advertisements

Similar presentations

Lesson 9-3: Cylinders and Cones

Advertisements

Chapter Area, Pythagorean Theorem, and Volume 14 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

EXAMPLE 3 Find the height of a cylinder COMPACT DISCS

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.

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

EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS

Find the volume of a sphere

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

EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. a. Area r = 2.5 cm SOLUTION Write formula for the area of a circle. = π (2.5)

Solve for unknown measures

( ) EXAMPLE 1 Evaluating Square Roots a. 36 = 6 6 because 2 = 36 . b.

EXAMPLE 2 Standardized Test Practice SOLUTION =+.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

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.

EXAMPLE 2 Standardized Test Practice SOLUTION =+.

Surface Area of Pyramids & Cones Section Objectives Find the surface area of pyramids Find the surface area of cones.

Surface Area of Cones Lesson 15. Write the surface area formula for each solid. 1. Prism 2. Cylinder 3. Pyramid 4. Find the surface area of each solid.

EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 = Write formula. l.

EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 = Write formula. l.

Find the area of each circle.

Standardized Test Practice EXAMPLE 3 Use the formula for the area of a rectangle, A = lw, with l = 18 inches and w = 11 inches. SOLUTION.

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

Section 7.2 – The Quadratic Formula. The solutions to are The Quadratic Formula

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.

10-4 Surface Areas of Pyramids

Lesson 12-5, 6, 13-2 Cones & Pyramids. Objectives Find lateral areas of regular pyramids Find surface areas of regular pyramids Find the volume of pyramids.

Surface Area and Volume of Cones

Section 12.3 Surface Area of Pyramids and Cones. Pyramid: polyhedron with one base lateral faces- triangles Slant Height: altitude of any lateral face.

Surface Areas of Pyramids and 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)

10-4 Surface Areas of Pyramids and Cones

Use the formula for circumference

Section 12.3 Surface Areas of Pyramids and Cones.

GEOMETRY HELP Find the volume of a square pyramid with base edges 15 cm and height 22 cm. Because the base is a square, B = = 225. V = BhUse the.

Find lateral areas of cones. Find surface areas of cones.

Volume of Pyramids & Cones

Warm Up. Difference between a prism and a pyramid.

 Lateral Surface Area : S = ½ P l  P represents the perimeter of the base and l represents the slant height  Total Surface Area : S = ½ P l + B 

Surface Area of Pyramids and Cones Surface Area of a Pyramid.

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)

1 Cylinders and Cones. 2 Surface Area (SA) = ph + 2B = 2πrh + 2πr 2 Cylinders are right prisms with circular bases. Therefore, the formulas for prisms.

12.6 Surface Areas of Cones. Objectives  Find lateral areas of cones.  Find surface areas of cones.

Lesson 5 Menu 1.Find the surface area of the regular pyramid shown. Round to the nearest tenth if necessary. 2.Find the surface area of the regular pyramid.

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 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.

Solve for unknown measures

Find the surface area of a sphere

The perimeter p of the square base is 4 X 7.5 ft, or 30 ft.

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.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

 Find lateral areas of cones.  Find surface areas of cones.

S URFACE A REA OF P YRAMIDS AND C ONES Section 9.3.

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

Pyramid – a polyhedron with one base (a polygon) and triangular lateral faces that meet at a common vertex. Regular Pyramid – a pyramid with a regular.

12.3 Surface Area of Pyramids and Cones

Calculate Surface Area of Pyramids & Cones

Surface Area of Pyramids and Cones

10-4 Surface Areas of Pyramids

Surface Area of Pyramids, Cones and Spheres

Find the surface area of a sphere

Surface Area of Pyramids, Cones and Spheres

Lateral Area & Surface Area Of Pyramids & Cones

10-4 Surface Areas of Pyramids

Find the surface area of a sphere

Surface Area of Pyramids, Cones and Spheres

14 Chapter Area, Pythagorean Theorem, and Volume

Lesson 9-3: Cylinders and Cones

11.3 Pyramids and Cones.

Presentation transcript:

Standardized Test Practice EXAMPLE 3 Standardized Test Practice SOLUTION To find the slant height l of the right cone, use the Pythagorean Theorem. l2 = h2+ r 2 Write formula. l2 = 82 + 62 Substitute. l = 10 Find positive square root.

Standardized Test Practice EXAMPLE 3 Standardized Test Practice Use the formula for the surface area of a right cone. S = πr2 + πrl Formula for surface area of a right cone = π(62) + π(6)(10) Substitute. = 96π Simplify. The correct answer is B. ANSWER

EXAMPLE 4 Find the lateral area of a cone TRAFFIC CONE The traffic cone can be approximated by a right cone with radius 5.7 inches and height 18 inches. Find the approximate lateral area of the traffic cone. SOLUTION To find the slant height l, use the Pythagorean Theorem. l2 = 182 + (5.7)2, so l ≈ 18.9 inches.

Find the lateral area of a cone EXAMPLE 4 Find the lateral area of a cone Find the lateral area. Lateral area = πrl Write formula. = π(5.7)(18.9) Substitute known values. ≈ 338.4 Simplify and use a calculator. The lateral area of the traffic cone is about 338.4 square inches. ANSWER

GUIDED PRACTICE for Examples 3 and 4 3. Find the lateral area of the right cone shown. SOLUTION To find the slant height l use the Pythagorean theorem l2 = 202 = 152 ,so l = 25 yd Find the lateral area

The lateral area of the right cone is 1178 yd2 ANSWER GUIDED PRACTICE for Examples 3 and 4 Lateral area = πrl Write formula. = π(15)(25) Substitute known values. ≈ 1178 Simplify and use a calculator. The lateral area of the right cone is 1178 yd2 ANSWER

4. Find the surface area of the right cone shown. GUIDED PRACTICE for Examples 3 and 4 4. Find the surface area of the right cone shown. SOLUTION S = πr2 + πrl Formula for surface area of a right cone = π(15)+ π(15)(25) Substitute. = 1885 Simplify. The surface area of the right cone is 1885yd2 ANSWER