
Find the height of the cone if the slant height h is 34cm and base diameter is 32cm.
Answer
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Hint: First, we will consider the height of the cone as h1. Then we will find the radius of the cone by using the formula . Then we will use the formula . On putting the values and on solving, we will get the answer. Here the formula used will be . Thus, we will get the height of the cone.
Complete step-by-step answer:
Here, we will first draw the diagram of cones with all dimensions given. So, diagram is as given below:
We have slant height h, diameter d as 32cm and we have assumed height of cone to be h1.
So, to find height of cone, the formula to be used is given as . So, we will first find the radius of the cone which can be given as .
On putting the value, we get as
Radius
Now, again substituting the value in the equation . So, we get as
Now, we will take squares on both sides, we will get as
Now, we will make h1 as subject so, we get as
Now, this above equation is in form . So, here a is 34 and b is 16. So, on using this formula, we get as
On further solving, we get as
Now, taking square root on both sides, we get as
Now, we can write this as
Thus, the height of the cone is 30cm.
Note: Students should remember one formula which is used to find either radius, height or slant height which is given as . Also, mistakes happen in calculation so, be careful while solving the equation in order to avoid mistakes. Do not forget to convert diameter into radius otherwise the answer will be completely wrong.
Complete step-by-step answer:
Here, we will first draw the diagram of cones with all dimensions given. So, diagram is as given below:

We have slant height h, diameter d as 32cm and we have assumed height of cone to be h1.
So, to find height of cone, the formula to be used is given as
On putting the value, we get as
Radius

Now, again substituting the value in the equation
Now, we will take squares on both sides, we will get as
Now, we will make h1 as subject so, we get as
Now, this above equation is in form
On further solving, we get as
Now, taking square root on both sides, we get as
Now, we can write this as
Thus, the height of the cone is 30cm.
Note: Students should remember one formula which is used to find either radius, height or slant height which is given as
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