the slant height of the frustum of a cone is 5cm.if the difference between the radii of its circular ends is 4cm.write the height of the frustum.
plz this question.
make a sketch of its cross section and draw in the height
I see a right -angled triangle with height h, so that
h^2 + 4^2 = 5^2
h^2 = 25-16 = 9
h = 3
ahh, the infamous 3-4-5 right-angled triangle
To find the height of the frustum, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the frustum (the hypotenuse) is given as 5 cm, and the difference between the radii of its circular ends is given as 4 cm.
Let's denote the radius of the larger circular end as R, and the radius of the smaller circular end as r. The height of the frustum can be represented as h.
Now, consider a right triangle formed by the slant height, the height, and the segment connecting the centers of the circular ends.
Using the Pythagorean theorem, we have:
(R - r)^2 + h^2 = 5^2
Expanding this expression, we get:
R^2 - 2Rr + r^2 + h^2 = 25
We also know that the difference between the radii of the circular ends is 4 cm, so we have:
R - r = 4
Solving this equation for R or r, we can substitute it back into the previous equation to find h.
Let's solve for r:
R - r = 4
r = R - 4
Substituting this value back into the previous equation, we get:
R^2 - 2R(R - 4) + (R - 4)^2 + h^2 = 25
Expanding and rearranging the terms, we have:
R^2 - 2R(R - 4) + R^2 - 8R + 16 + h^2 = 25
2R^2 - 2R^2 + 8R - 16 + h^2 = 25
8R + h^2 - 16 = 25
8R + h^2 = 41
Now, we have an equation with two variables, R and h. We need additional information to solve for both variables simultaneously.
Is there any additional information given in the question?