Work out the volume of the cone, giving your answer accurate to two decimal places.
Let′s begin by recalling the formula for calculating the volume of a cone. It′s one-third 𝜋𝑟 squared ℎ, where 𝑟 is the radius of the circle at the base of the cone and ℎ is its perpendicular height. That′s the distance between the center of the circular base of the cone and its point or apex. We can remember this formula by remembering that the volume of a cone is one-third of the volume of the cylinder that surrounds it. The volume of a cylinder is 𝜋𝑟 squared ℎ, and the volume of a cone is one-third of this.
Looking at the diagram we′ve been given, we observe that the radius of the cone, that′s 𝑟, is three and the height of the cone, ℎ, is 10. So, substituting these values into the formula, we have that the volume of this cone is one-third multiplied by 𝜋 multiplied by three squared multiplied by 10. Three squared is nine, and multiplying by 10 gives 90, and then multiplying by one-third or dividing by three gives 30. So, this simplifies to 30𝜋.
Now, if we wanted an exact answer or if we didn′t have a calculator, we could leave our answer in this form, as a multiple of 𝜋. But as we′ve been asked to give the volume accurate to two decimal places, we′ll go on and evaluate this as a decimal. Using a calculator, it is 94.2477 continuing, and we′ll then round to two decimal places. As the value in the third decimal place is a seven, we′re rounding up to 94.25. We weren′t given any units for the lengths in the question. So, the units for the volume will be general cubic units.
So, accurate to two decimal places, we′ve found that the volume of this cone is 94.25 cubic units.