Previous Volume Applications Find the volume of each figure. 1.rectangular prism with length 20 cm, width 15 cm, and height 12 cm 20cm 15cm 12cm V = Bh V = lwh V =20cm(15cm)12cm V = 3600 cm 3 2. triangular prism with a height of 6 cm and a triangular base with base length 4.1 cm and height 3.1 cm V = Bh V = (½bh)h V = (½)4.1cm(3.1)cm(6cm) V = cm 3

We had covered the volume formula for prisms. We started to talk about the parts of a circle and pi……… Where were we???

Circles Area and Cylinder Volume

A circle is the set of all points in a plane that are the same distance from a given point, called the center. Circles are named by the point at the center. Center B This would be called circle B. Discussion Review…..

A radius is a segment that connects the center to the circle. A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius. A tangent is a segment that touches the circle at only one point. Center Radius Diameter chord 2r = d Tangent An arc is part of the circle. A central angle is an angle whose vertex is the center of the circle.

Review: Parts of Circles S P W K M B 1. This is Circle _______ 2. Name two chords: 3. Which chord is the diameter? 4. Name three radii: S WP and KB KB SK SM SB 5. Name a central angle. Angle MSB or Angle MSK

Pi is the ratio between the circumference and the diameter. Pi is used to calculate both circumference and area. In plain words…..the distance around any circle is a little more than 3 times (3.14) the distance across the circle. C = 3.14 (diameter) C d =  C=  d

Finding Circle Area & Cylinder Volume Application

The formula for the area of a circle is A =  r 2. The area of a circle measures the region enclosed by the circumference This formula tells us to find the radius, square it (multiply it by itself) and then multiply by . A =  r 2. 8 mm A =  (8 mm)(8 mm) A = 3.14(64 mm 2 ) A = mm 2 6 mm A =  r 2. How do I get the radius? A = 3.14 (3mm) 2. A = 3.14(9)mm 2. A = 28.26mm 2. d=6 r=3

Solving in terms of pi. A =  r cm

The area of this circle is sq. cm. What is the radius? Start with the formula! = r sq. cm= (3.14) r 2 _______ ______

Use 3.14 for . 12 ft. A = ft 2 A = 3.14 (6ft) 2 A = (3.14)36ft 2 d = 12 r = m A = 36.3 m 2 A = 3.14 (3.4m) 2 A = (3.14)11.56m 2

Find the area in terms of pi. The diameter is 18 ft. d=18 r=9

To find the volume of a cylinder, you can use the same method as you did for prisms: volume of a cylinder = area of base  height The area of the circular base is r 2, so the formula is V = Bh V = (r 2 )h.

Compare and Contrast Why are we able to use the same formula for both of these objects? At what point do the substituted values differ? Why???????

Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. Write the formula. Replace  with 3.14, r with 4, and h with 7. Multiply. V  V = r 2 h V  3.14  4 2  7 The volume is about 352 ft 3.

Finding the Volume of a Cylinder 10 cm ÷ 2 = 5 cmFind the radius.Write the formula. Replace  with 3.14, r with 5, and h with 11. Multiply. V  V = r 2 h V  3.14  5 2  11 The volume is about 864 cm 3.

Cylinder Volume

Finding missing measures…….. This cylinder has a diameter of 4 inches. The volume is cubic inches. What is the height?

Finding missing measures…….. The volume of this cylinder is 1256 cubic meters. The height is 16 meters. What is the diameter?