b. find the lateral area of the cylinder c. If the radius is doubled, what happens to the volume?

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1 im: How do we find the volume and surface area of pyramids? o Now: If the radius and the height of a cylinder is 4 a. find the volume of the cylinder b. find the lateral area of the cylinder c. If the radius is doubled, what happens to the volume? If the height is doubled, what happens to the volume? 1. If the volume of a right circular cylinder is cubic cm, and the height is 8.2 cm, what is the radius of the base ( to the nearest tenth)? 2. cylindrical container 10 inches in diameter is required to hold 10 gallons of water. Find the height to the nearest tenth of an inch, if one gallon of water occupies 231 cubic inches of space. 3.

2 YRMI: ( polyhedron with a base that is a polygon and lateral faces that are triangles having the bases be the sides of the of the polygon as bases and all having a common vertex. Regular pyramid: a pyramid whose base is a regular polygon im: How do we explore the volume, lateral area, and surface area of pyramids and cones? Lateral rea Surface rea Volume

3 Model : The perimeter of the base of a regular square pyramid is 40cm and a lateral edge measures 13cm. Find a. The lateral area of the pyramid b. The height of the pyramid in radical form c. the volume of the pyramid rounded to the nearest tenth of a cubic centimeter IM: How do we explore volume, surface area of cones and spheres? NW: (a) The spire of the city hall is in the shape of a cone that has a circular base that is 20 feet in diameter. The slant height of the cone is 40 feet. How many whole gallons of paint will be needed to paint the spire if a gallon of paint will cover 350 square feet?

4 Model 2 : 1.Find the radius R of the original cone 2. Find the volume of the frustrum in terms of π 3. Find the lateral area of the original cone 1. Find the altitude of a pyramid with a rhombus as a base and diagonals of 4 in, and 6 in, and a volume of 3 cubic inches.

5 TRY. regular square pyramid has 12 as the measure of each edge of the base and the height of the pyramid is 8. Find a. the lateral area b. the total surface area c. the volume TRY 2: The altitude of a right circular cone makes an angle of 45 o with the slant height. If the radius of the base is 8 inches, what is the volume of the cone in terms of π? 3. What is the lateral area and the total surface area of a regular pyramid with the length of each edge equal to 6? Leave your answer in simplest radical form.

6 SHERE R SURFE RE = VLUME = im: How do we review circles, and spheres to review for the final exam? 1. iameter of the moon is 2,160 miles. Find the volume and surface area of the moon in terms of π. (SSUME THE MN IS SHERE)

7 1. iameter of the moon is 2,160 miles. Find the volume and surface area of the moon in terms of π. (SSUME THE MN IS SHERE) 2. Find the radius of the sphere (in terms of π) if a. Surface area = 84cm 2 b. Volume = 14.4 cubic inches

8 is the center of each circle Given: line which is tangent to circle at Tangent drawn to a circle is perpendicular to the radius drawn to the point of tangency The degree measure of a central angle is equal to the degree measure of the intercepted arc The measure of an inscribed angle is half the measure of the intercepted arc The measure of a tangent chord angle is half the measure of the intercepted arc R Given: Secant R, chord The measure of the secant chord angle is found by finding the measure of its supplement ( an inscribed angle) or by other methods E Given: hords, intersect at E Measure of a chord chord angle is half of the sum of the two intercepted arcs Given: Secants, intersecting at outside the circle The measure of a secant secant angle is half the difference of the two intercepted arcs (bigger smaller) Given: Tangent, secant that intersect at an exterior point The measure of a tangent secant angle is half of the difference of the two intercepted arcs R Given:Tangents R, and R intersecting at an exterior point R The measure of a tangent tangent angle is half of the difference of the two intercepted arcs The measure of a tangent tangent angle is supplementary to the minor intercepted arc

9 E Given: hord, and diameter intersect at E In a circle, if a diameter bisects the chord, then it is perpendicular to the chord In a circle, if a diameter is perpendicular to a chord, then it bisects the chord R Relationship between the line segments (Whole)(Exterior) = (Whole) (Exterior) E Relationship between the line segments (roduct of parts of chord 1 = product of parts of chord 2) In a circle, congruent chords intercept congruent arcs In a circle, congruent arcs are intercepted by congruent chords In a circle, parallel chords intercept two congruent arcs that lie between them