what is the height of a lamp whose two radii are 20cm and 30cm slant height is 40cm
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what is the height of a lamp whose two radii are 20cm and 30cm and slant height is 40cm respectively?
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To find the height of the lamp, we can use the concept of a right triangle and apply the Pythagorean theorem.
The radius of a cone represents one of the legs of the right triangle, the slant height represents the hypotenuse, and the height of the cone represents the other leg.
Let's label the given values:
- First radius (smaller radius): r1 = 20 cm
- Second radius (larger radius): r2 = 30 cm
- Slant height: s = 40 cm
- Height of the lamp: h (unknown)
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:
r1^2 + h^2 = s^2
Substituting the given values, we get:
20^2 + h^2 = 40^2
400 + h^2 = 1600
h^2 = 1600 - 400
h^2 = 1200
To solve for h, we take the square root of both sides:
√(h^2) = √1200
h = √1200
h ≈ 34.64 cm
Therefore, the height of the lamp is approximately 34.64 cm.
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what is the height of a lamp whose two radii are 20cm and 30cm and slant height is 40cm ?
Draw a side view. You can see that
(30-20)^2 + h^2 = 40^2