Surface area of cylinders & cones

Surface area of cylinders & cones

By Marcia Davis

Cylinder Volume

Cylinder Surface Area

Fill in the Blank

The cylinder in the diagram has a diameter of 8 in and height of 12 in.

What is the base area of the cylinder? Write in terms of pi.

______ $$in^2$$  

Fill in the Blank

Find the lateral (rectangle) area of the cylinder. Give your answer in terms of pi.

________ $$in^2$$  

Multiple Choice

What is the total Surface Area of the cylinder?

• $$112\pi\ \ in^2$$

• $$128\pi\ \ in^2$$

• $$192\pi\ \ in^2$$

• $$768\pi\ \ in^2$$

Fill in the Blank

Find the surface area of the cylinder. You may use a calculator and round your answer to the nearest TENTH (1 decimal place) ________ $$ft^2$$   

Surface Area of Cones

• We need to separate into base and lateral area.

• Notice with a cone, we only have one base (circle)

• The lateral area is similar to that of a cylinder, but we won't use circumference, like we did for the cylinders.

Surface Area

Try this on your own

Multiple Select

radius = 4 cm and slant height = 5 cm

$$\pi$$  rl + $$\pi$$  r²

$$\pi$$  (4 cm)(5 cm) + $$\pi$$  (4 cm)²

20 $$\pi$$  cm² + 16 $$\pi$$  cm²

is what? Mark all that apply.

• 113.1 cm²

• 36 cm²

• 36 $$\pi$$  cm²

• 113.1 $$\pi$$  cm²

What if we have the true height instead of our slant height?

• Can we find the slant height somehow? (What kind of triangle does it make?)

• Use pythagorean theorem to find the hypotenuse (slant height)!

Fill in the Blank

Find the SLANT HEIGHT of this cone: Round to nearest tenth