Surface Area Pyramids Cylinders Spheres and Cones Math

Surface Area - Pyramids, Cylinders, Spheres and Cones Math 20 -3 Poulin

Review: Working with Circles • This can be divided into parts: a rectangle 112. 6 cm long and 58. 4 cm ft wide, and two semi circles, each with a diameter of 58. 4 cm. The two semi-circles will make a full circle.

Ex. Work •

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 •

Ex. Work

Pyramids • A pyramid is a threedimensional 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 •

Ex. Work