A cone has slant height of 29cm and a circular base of diameter 42cm.calculate the vertical height of the cone.
I need a help pls
Make a sketch of the cross-section of the cone to realize that
you are simply faced with Pythagoras, the slant height being the hypotenuse.
let the height be h
h^2 + 21^2 = 19^2
h^2 = 841 - 441 = 400
h = √400 = 20 cm
Well, let me put on my funny hat and calculate the vertical height of the cone for you! Now, imagine this - the cone is like a party hat, trying to reach for the stars. So, let's find out how tall this aspiring party hat is.
We'll use a little bit of triangle magic here. The slant height is like the circus tightrope that connects the tip of the party hat to the edge of the base. And the vertical height is like the distance from the tip to the center of the base.
Now, the slant height acts as the hypotenuse of a right triangle formed with the vertical height and the radius of the base. Since the diameter of the base is 42 cm, the radius is half of that, which is 21 cm.
Using the Pythagorean theorem (don't worry, it's just a fancy formula, not a dangerous math experiment), we'll have:
vertical height^2 + radius^2 = slant height^2
So, let's plug in the numbers:
vertical height^2 + 21^2 = 29^2
vertical height^2 + 441 = 841
Subtracting 441 from both sides, we get:
vertical height^2 = 400
Taking the square root of both sides, we find:
vertical height = 20 cm
Voila! The vertical height of the cone is 20 cm, just like that! Now, you can imagine the cone wearing its party hat proudly and reaching for the stars.
To find the vertical height of the cone, we can use the Pythagorean Theorem. The slant height of the cone (l) and the vertical height of the cone (h) are the legs of a right triangle, and the radius of the base (r) is the hypotenuse.
Let's calculate the radius of the base first. We know that the diameter (d) is 42 cm. The radius (r) is half of the diameter, so:
r = d/2
= 42 cm / 2
= 21 cm
Now, we can use the Pythagorean Theorem to find the vertical height. The equation is:
l^2 = r^2 + h^2
Substituting the given values into the equation:
29^2 = 21^2 + h^2
841 = 441 + h^2
h^2 = 841 - 441
h^2 = 400
To solve for h, we take the square root of both sides of the equation:
h = √400
= 20 cm
Therefore, the vertical height of the cone is 20 cm.
To find the vertical height of the cone, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the cone acts as the hypotenuse, and the vertical height and the radius of the base act as the other two sides. To use the theorem, you'll need to find the radius of the base.
The diameter given is 42cm, so the radius (r) is half of it, which is 42/2 = 21cm.
Using the Pythagorean theorem:
(slant height)^2 = (vertical height)^2 + (radius)^2
Substituting the given values:
29^2 = (vertical height)^2 + 21^2
Simplifying:
841 = (vertical height)^2 + 441
Rearranging the equation:
(vertical height)^2 = 841 - 441
(vertical height)^2 = 400
Taking the square root of both sides:
vertical height = √400
vertical height = 20 cm
Therefore, the vertical height of the cone is 20 cm.