The total surface area of a right circular cone is 90πcm². If the radius of the base of cone is 5cm,find the night of the cone
Answers
Total surface of a cone = πrl + πr²
so πrl + πr² = 90π
=>5πl + 25π = 90π
=>5πL = 65π
=> L = 65π/5π = 13cm
but L = √r²+h²
=>13 =√(25 + h²)
=>169 = 25 + h²
=>h² = 144
=>h=12
so height is equal to 12cm
hope it helps mark as brainliest
Given - Total Surface area and radius
Find - Height of cone
Solution - The height of the cone is - 3.4 centimetres
The total surface area of the cone is calculated by the formula -
Total surface area = πrl² + πr²
Keep the values in the formula to find the value of length or hypotenuse.
90π = πr(l² + r)
90 = 5(l² + 5)
18 = l² + 5
l² = 13
Now, find the height of the cone.
length² = perpendicular² + base²
13 = perpendicular² + 5²
Perpendicular² = 25 - 13
Perpendicular² = 12
Perpendicular = 3.4 centimetres.
Thus, the height of the cone is 3.4 centimetres