10-9 Volume of Cylinders Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Course Finding Volume 6 th HOMEWORK Answers Page 536 #1-6

Course Volume of Cylinders 6 th Grade Math HOMEWORK Page 540 #1-3 and #6-8 Due Monday!

Our Learning Goal Students will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface area and volume of 3D shapes.

Our Learning Goal Assignments Learn to find the perimeter and missing side lengths of a polygon. Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms. Learn to break a polygon into simpler parts to find its area. Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure. Learn to identify the parts of a circle and to find the circumference and area of a circle. Learn to name solid figures. Learn to find the surface areas of prisms, pyramids, and cylinders. Learn to estimate and find the volumes of rectangular prisms and triangular prisms. Learn to find volumes of cylinders.

Warm Up Find the volume of each figure described. Course Volume of Cylinders cm 3 1,320 cm 3 1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm 2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm

Problem of the Day The height of a box is half its width. The length is 12 in. longer than its width. If the volume of the box is 28 in, what are the dimensions of the box? 1 in.  2 in.  14 in. 3 Course Volume of Cylinders

Today’s Learning Goal Assignment Learn to find volumes of cylinders. Course Volume of Cylinders

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

Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. A. 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. Course Volume of Cylinders

Try This: Example 1A Find the volume V of each cylinder to the nearest cubic unit. A. Multiply. V  The volume is about 565 ft 3. 6 ft 5 ft Write the formula. Replace  with 3.14, r with 6, and h with 5. V = r 2 h V  3.14  6 2  5 Course Volume of Cylinders

Additional Example 1B: Finding the Volume of a Cylinder B. 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. Course Volume of Cylinders

Try This: Example 1B B. Multiply. V  cm ÷ 2 = 4 cm The volume is about 301 cm 3. Find the radius. 8 cm 6 cm Write the formula. Replace  with 3.14, r with 4, and h with 16. V = r 2 h V  3.14  4 2  6 Course Volume of Cylinders

Additional Example 1C: Finding the Volume of a Cylinder C. Find the radius. r = + 4 h 3 __ r = + 4 = __ Substitute 9 for h.Write the formula. Replace  with 3.14, r with 7, and h with 9. Multiply. V  1, V = r 2 h V  3.14  7 2  9 The volume is about 1,385 in 3. Course Volume of Cylinders

Try This: Example 1C C. Multiply. V  The volume is about 1231 in 3. Find the radius. r = + 5 h 4 __ r = + 5 = __ Substitute 8 for h. r = + 5 h = 8 in h 4 Write the formula. Replace  with 3.14, r with 7, and h with 8. V = r 2 h V  3.14  7 2  8 Course Volume of Cylinders

Additional Example 2A: Application Ali has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder- shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch. A. Ali’s pencil holder Write the formula. Replace  with 3.14, r with 1.5, and h with 5. Multiply. V  in. ÷ 2 = 1.5 in. V  3.14   5 The volume of Ali’s pencil holder is about 35 in 3. Find the radius. V = r 2 h Course Volume of Cylinders

Additional Example 2B: Application B. Scott’s pencil holder Write the formula.Multiply.4 in. ÷ 2 = 2 in. The volume of Scott’s pencil holder is about 75 in 3. Find the radius. V = r 2 h Replace  with, r with 2, and h with __ V   22  6V   22  __ V  = ___ 3 7 __ Course Volume of Cylinders

Try This: Example 2A Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch. A. Sara’s sunglasses case Write the formula. Replace  with 3.14, r with 1.5, and h with 6. Multiply. V  in. ÷ 2 = 1.5 in. V  3.14   6 The volume of Sara’s sunglasses case is about 42 in 3. Find the radius. V = r 2 h Course Volume of Cylinders

Try This: Example 2B B. Ulysses’ pencil holder Write the formula.Multiply.4 in. ÷ 2 = 2 in. The volume of Scott’s pencil holder is about 75 in 3. Find the radius. V = r 2 h Replace  with, r with 2, and h with __ V   2 2  __ V = 88 Course Volume of Cylinders

Additional Example 3A & 3B: Comparing Volumes of Cylinders Find which cylinder has the greater volume. Cylinder 1: V  3.14   12 V = r 2 h V  cm 3 Cylinder 2: V  3.14  3 2  6 V = r 2 h V  cm 3 Cylinder 2 has the greater volume because cm 3 > cm 3. Course Volume of Cylinders

Try This: Example 3A & 3B Find which cylinder has the greater volume. Cylinder 1: V  3.14   10 V = r 2 h V  cm 3 Cylinder 2: V  3.14  2 2  4 V = r 2 h V  cm 3 Cylinder 1 has the greater volume because cm 3 > cm cm 2.5 cm 4 cm Course Volume of Cylinders

Lesson Quiz Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for . Insert Lesson Title Here cylinder B 1, ft ft ft 3 1, ft 3 Course Volume of Cylinders 1. radius = 9 ft, height = 4 ft 2. radius = 3.2 ft, height = 6 ft 3. Which cylinder has a greater volume? a. radius 5.6 ft and height 12 ft b. radius 9.1 ft and height 6 ft