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The slant height of a cone is 26 cm and base diameter is 20 cm. Its height is
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Explanation:
The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by:
l² = r² + h²,
where:
– l is the slant height,
– r is the radius of the base,
– h is the height of the cone.
From the problem:
– The slant height (l) is 26 cm,
– The diameter of the base is 20 cm, so the radius (r) is:
r = Diameter / 2 = 20 / 2 = 10 cm.
Substitute the values of l = 26 cm and r = 10 cm into the formula:
l² = r² + h².
Rearrange to solve for h²:
h² = l² – r².
Substitute the values:
h² = 26² – 10²,
h² = 676 – 100,
h² = 576.
Take the square root of both sides:
h = √576,
h = 24 cm.
Thus, the height of the cone is 24 cm, which corresponds to option a) 24.
This question related to Chapter 11 Mathematics Class 9th NCERT. From the Chapter 11 Surface area and Volumes. Probability. Give answer according to your understanding.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-9/maths/
Explanation:
The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by:
l² = r² + h²,
where:
– l is the slant height,
– r is the radius of the base,
– h is the height of the cone.
From the problem:
– The slant height (l) is 26 cm,
– The diameter of the base is 20 cm, so the radius (r) is:
r = Diameter / 2 = 20 / 2 = 10 cm.
Substitute the values of l = 26 cm and r = 10 cm into the formula:
l² = r² + h².
Rearrange to solve for h²:
h² = l² – r².
Substitute the values:
h² = 26² – 10²,
h² = 676 – 100,
h² = 576.
Take the square root of both sides:
h = √576,
h = 24 cm.
Thus, the height of the cone is 24 cm, which corresponds to option a) 24.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-9/maths/