Download Surface Area - Pyramids, Cylinders, Spheres and Cones

Surface Area -
Pyramids, Cylinders,
Spheres and Cones
Workplace 20
Poulin
Review: Working with Circles
• This can be divided into parts: a rectangle 112.6cm long and 58.4cm ft wide, and two semi
circles, each with a diameter of 58.4cm. The two semi-circles will make a full circle.
Ex. Work
•𝐴= 𝐿 𝑤
Cylinders
• A cylinder is like a prism, but has
circular bases. To find the
surface area, you have to find
the area of the two circles and
the area between them. If you
draw a net of a cylinder, you will
find it is made up of 2 circles and
a rectangle. The length of the
rectangle will be the
circumference of the circle , and
the width will be the height of
the cylinder.
Cylinder example
• Steps
• Find the area of the circular base
• 𝐴 = 𝜋𝑟 2
• Find the circumference of the cylinder
• 𝐶 = 2𝜋𝑟
• Find the area of the lateral face
• 𝐴 = 𝐶𝑥ℎ
• Calculate the total surface area
• 𝑆𝐴 = 2 𝐴1 + 𝐴2
Ex. Work
Pyramids
• A pyramid is a
three-dimensional
object with a
polygonal base and
lateral sides that
are triangles. The
triangles meet at a
point called the
apex.
• Right pyramid – the
apex is directly
above the center of
the base.
Pyramid net
Pyramid Example
• Steps to finding surface area
• Identify base and height
• Find the ‘slant height’ of the pyramid using the Pythagorean
Theorem
• Find the height of the triangles that form the lateral faces – or
the slant height of the pyramid – you must use a triangle as shown
on the next slide.
• Once you have found 2 sides, you can use Pythagorean Theorem to
find the hypotenuse, which is the slant height.
• The surface area of the pyramid = the area of the square base
plus the area of the four triangles.
Ex. Cont.
Find the surface area of the square based
triangle.
• Step 1 – finding height of the triangles
that form the lateral faces – or the
slant height of the pyramid.
• Step 2 - Use Pythagorean Theorem
• Step 3 - Use area of triangles + base to
find total surface area
Ex. Work
Cones
• A cone is like a pyramid, but it has a
circular base. The net of a cone is a
sector of a large circle, and the
circular bas of a cone.
• The surface area of the lateral area
of the cone (the area not including
the base) can be calculated using
this formula, where ‘r’ is the radius
of the circular base and ‘s’ is the
slant height of the lateral base.
Cone Example
• Steps
• Calculate the area
of the circular
base 𝐴 = 𝜋𝑟 2
• Calculate the area
of the lateral 𝐴
= 𝜋𝑟𝑠
• Calculate the
total surface area
𝑆𝐴 = 𝐴1 + 𝐴2
Ex. Work