the curved surface area of right circular coren is 196 cm and the radius base is 7 cm find the volume of the cone (take π = and √2=1.41) with solution
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The answer is given below :
Given that,
curved surface area = π × radius of the base × slant height
=> π × 7 × slant height = 196
=> slant height = 98/11
So, slant height = 98/11 cm
Now,
(slant height)² = (height)² + (radius of the base)²
=> (98/11)² = (height)² + (7)²
=> (height)² = (98/11)² - (7)²
So, height = √[(98/11)² - (7)²] cm, where we take the positive value only.
[NB : height refers to the height of the cone]
Thus, the volume of the cone
= 1/3 × π × (radius of the base)² × height
= 1/3 × π × 7² × √[(98/11)² - (7)²] cm³
= 282.78 cm³ (approximately)
Thank you for your question.
Given that,
curved surface area = π × radius of the base × slant height
=> π × 7 × slant height = 196
=> slant height = 98/11
So, slant height = 98/11 cm
Now,
(slant height)² = (height)² + (radius of the base)²
=> (98/11)² = (height)² + (7)²
=> (height)² = (98/11)² - (7)²
So, height = √[(98/11)² - (7)²] cm, where we take the positive value only.
[NB : height refers to the height of the cone]
Thus, the volume of the cone
= 1/3 × π × (radius of the base)² × height
= 1/3 × π × 7² × √[(98/11)² - (7)²] cm³
= 282.78 cm³ (approximately)
Thank you for your question.
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