T Madas Cylinders and Cones Axis Vertex Generator

Cylinders and Cones Axis Vertex Generator Slant Height Radius Base © T Madas

The Volume of a Cylinder A cylinder is a Prism r whose cross section

Calculate the volume of these cylinders 40 cm V = x-sectional Area x height

Calculate the volume of these cylinders 35 cm V =πr 2 x h V

The Surface Area of a Cylinder © T Madas

Calculate the Surface Area of these Cylinders 40 cm S = 2π r h

Calculate the Surface Area of these Cylinders 50 cm S = 2π r h

The Volume of a Cone It can be shown that for a cone: V=

8 cm 9 cm Calculate the volume of these cones 6 cm 4 cm

12 cm 9 cm Calculate the volume of these cones 5 cm 3 cm

A cylinder is shown below. The radius of its base is 6 cm and

A tank without a lid is in the shape of a cylinder. The radius

A can without a lid is in the shape of a cylinder. The radius

Find the volume of this compound shape in terms of π Using Pythagoras Theorem:

Find the volume of this compound shape in terms of π The volume of

Find the volume of this compound shape in terms of π Total volume of

Slides: 36

Download presentation

Cylinders and Cones Axis Vertex Generator Slant Height Radius Base © T Madas

Volume of a Cylinder © T Madas

The Volume of a Cylinder A cylinder is a Prism r whose cross section is a c ircle h V = Base Area x Height = πr 2 x h © T Madas

Calculate the volume of these cylinders 40 cm V = x-sectional Area x height V =πr 2 x h V = π x 102 x 40 V ≈ 12566 cm 3 [n. w. n. ] 22 m 5 m 10 cm V = x-sectional Area x height V =πr 2 x h V = π x 52 x 22 V ≈ 1728 m 3 [n. w. n. ] © T Madas

Calculate the volume of these cylinders 35 cm V =πr 2 x h V = π x 122 x 35 V ≈ 15834 cm 3 [n. w. n. ] 18 m 4 m 12 cm V =πr 2 x h V = π x 42 x 18 V ≈ 905 m 3 [n. w. n. ] © T Madas

Surface Area of a Cylinder © T Madas

The Surface Area of a Cylinder © T Madas

Calculate the Surface Area of these Cylinders 40 cm S = 2π r h + 2π r 2 22 m 5 m 10 cm S = 2π r h + 2π r 2 S = 2 x π x 10 x 40 + 2 x π x 102 S = 2 x π x 5 x 22 + 2 x π x 52 S ≈ 2513. 27 + 628. 32 S ≈ 691. 15 + 157. 08 S ≈ 3142 cm 2 [n. w. n. ] S ≈ 848 m 2 [n. w. n. ] © T Madas

Calculate the Surface Area of these Cylinders 50 cm S = 2π r h + 2π r 2 14 m 4 m 15 cm S = 2π r h + 2π r 2 S = 2 x π x 15 x 50 + 2 x π x 152 S = 2 x π x 4 x 14 + 2 x π x 42 S ≈ 4712. 39 + 1413. 72 S ≈ 351. 86 + 100. 53 S ≈ 6126 cm 2 [n. w. n. ] S ≈ 452 m 2 [n. w. n. ] © T Madas

Volume of a Cone © T Madas

The Volume of a Cone It can be shown that for a cone: V= Base Area x Height h r © T Madas

8 cm 9 cm Calculate the volume of these cones 6 cm 4 cm V= 1 3 πr h = 13 x 2 2 π x 4 x 9 ≈ 151 cm 3 V= 1 3 π r 2 h 2 = 13 x π x 6 x 8 ≈ 302 cm 3 © T Madas

12 cm 9 cm Calculate the volume of these cones 5 cm 3 cm V= 1 3 π r 2 h 2 = 13 x π x 3 x 12 V= 1 3 π r 2 h 2 = 13 x π x 5 x 9 ≈ 236 cm 3 ≈ 113 cm 3 © T Madas

A cylinder is shown below. The radius of its base is 6 cm and has a volume of 1000 cm 3. Calculate its surface area to 3 significant figures. Volume = base area x height 8. 84 cm 6 cm h 1000 = 6 x π x h 1000 ≈ 113. 1 x h h ≈ 1000 ÷ 113. 1 h ≈ 8. 84 cm © T Madas

A cylinder is shown below. The radius of its base is 6 cm and has a volume of 1000 cm 3. Calculate its surface area to 3 significant figures. Surface Area: 6 x π x 2 ≈ 226. 2 cm 2 8. 84 cm 6 cm 2 x 6 x π x 8. 84 ≈ 333. 3 cm 2 559. 5 cm 2 8. 84 cm Circumference of circle 560 cm 2 [ 3 s. f. ] © T Madas

A tank without a lid is in the shape of a cylinder. The radius of its base is 30 cm and has a capacity of 225 litres. Calculate its surface area, to 2 significant figures. 30 cm 79. 6 cm 1 litre = 1000 cm 3 h 225 litres = 225000 cm 3 Volume = base area x height 225000 = 30 x π x h 225000 ≈ 2827 x h h ≈ 225000 ÷ 2827 h ≈ 79. 6 cm © T Madas

A tank without a lid is in the shape of a cylinder. The radius of its base is 30 cm and has a capacity of 225 litres. Calculate its surface area, to 2 significant figures. 30 x π ≈ 2827 cm 2 79. 6 cm 30 cm Surface Area: h 2 x 30 x π x 79. 6 ≈ 15004 cm 2 17831 cm 2 79. 6 cm Circumference of circle 18000 cm 2 [ 2 s. f. ] © T Madas

A can without a lid is in the shape of a cylinder. The radius of its base is 4 cm and has a capacity of 192π cm 3. Calculate its surface area in terms of π. Volume = base area x height 12 cm 4 cm h 192π = 4 x π x h 192π = 16π h = 12 cm © T Madas

A can without a lid is in the shape of a cylinder. The radius of its base is 4 cm and has a capacity of 192π cm 3. Calculate its surface area in terms of π. Surface Area: 4 cm 12 cm 4 xπ ≈ 16π cm 2 2 x 4 x π x 12 ≈ 96π cm 2 112π cm 2 12 cm Circumference of circle © T Madas