Video Transcript
Find the total surface area of the
right cone approximated to the nearest two decimal places.
We’re told on the diagram that the
height of the cone is 14.5 centimetres. And its slant height is 16.5
centimetres. The radius is currently
unknown. We can calculate the length of the
radius by using Pythagoras’s theorem. This states that 𝑎 squared plus 𝑏
squared is equal to 𝑐 squared, where 𝑐 is the longest side of a right triangle,
known as the hypotenuse. Substituting in our values gives us
𝑟 squared plus 14.5 squared is equal to 16.5 squared. Subtracting 14.5 squared from both
sides gives us 𝑟 squared is equal to 16.5 squared minus 14.5 squared. Square-rooting both sides of this
equation gives us 𝑟 is equal to 16.5 squared minus 14.5 squared. This is equal to the square root of
62.
For accuracy, we will leave our
answer in this form at present. We were asked to calculate the
total surface area of the cone. A cone has two surfaces, a curved
surface and a base. Therefore, the total surface area
is equal to the area of the curved surface plus the area of the base. The area of the curved or lateral
surface is equal to 𝜋𝑟𝑙. We multiply 𝜋 by the radius by the
slant height. As the base is a circle, we work
out the area of the base by multiplying 𝜋 by the radius squared. Substituting in our values for the
radius and slant height gives us 𝜋 multiplied by the square root of 62 multiplied
by 16.5 plus 𝜋 multiplied by the square root of 62 squared.
The square root of 62 squared is
just equal to 62. As we need to calculate this to two
decimal places and not in terms of 𝜋, we can type this calculation into our
calculator. This gives us an answer of
602.93801 and so on. The eight in the thousandths column
is the deciding number. When this digit is greater than or
equal to five, we round up. The total surface area of the cone
to two decimal places is 602.94 square centimetres. Any surface area will be measured
in square units.
