A paper cone cup beside a water cooler has a diameter of 6 centimeters and a slant length of 9 centimeters. What is the approximate height,h, of the cup?
A 3 radical 5 centimeters
B 6 radical 2 centimeters
C 3 radical 10 centimeters
D 7 radical 2 centimeters
make a side view sketch and you will see that
h^2 + 3^2 = 9^2
solve for h
btw, your choices are not approximate heights, they are exact heights
um they aren"t exact bc of the radicals thank you very much -_-
To find the height of the cone cup, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the slant length) is equal to the sum of the squares of the other two sides.
In this case, the slant length is 9 centimeters and the radius (half of the diameter) is 3 centimeters. Let's consider the height of the cone cup as 'h'. We can draw a right triangle where the slant length is the hypotenuse, one side is the height 'h', and the other side is the radius of the base:
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/ |
h/ |
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radius
Applying the Pythagorean theorem, we have:
radius² + h² = slant length²
(3 cm)² + h² = (9 cm)²
9 cm² + h² = 81 cm²
Simplifying the equation:
h² = 81 cm² - 9 cm²
h² = 72 cm²
Taking the square root of both sides to find the value of h:
h ≈ √72 cm
Simplifying the square root of 72:
h ≈ √(36 x 2) cm
h ≈ √36 cm x √2
h ≈ 6 cm x √2
So, the approximate height of the cone cup, h, is 6√2 centimeters.
Therefore, the answer is option B: 6√2 centimeters.