A sphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is H inches above t
he first plane. The resulting portion of the sphere between the two planes is called a spherical segment; see the picture: In Math 125, you will show that the volume V of the spherical segment is given by this formula (which we will assume): V = (π/3)H(27 – H2). Give EXACT ANSWERS to the questions below. (a) Find the volume of the spherical segment if H=1: (b) Find the rate of change of the volume with respect to H of the spherical segment at H=1: (c) Use the tangent line approximation at H=1 to estimate the value of H that will yield a spherical segment having volume 25 cubic inches:
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Length of the radius of the cone is equals to 5 cm.
<h3>What is right circular cone?</h3>
" A right circular cone is the 3 dimensional solid shape, which has an axis that is perpendicular to its circular base."
Formula used
Pythagoras theorem
(Hypotenuse)² = (adjacent side)² + (opposite side)²
According to the question,
Slant height 'l' of the cone = 13cm
height 'h' of the cone = 12cm
Let 'r' be the radius of the base of the cone.
As per the diagram,
InΔABC,
Apply Pythagoras theorem, we get
(l)² = (h)² +(r)²
Substitute the values of 'l' and 'h' in the formula we get,
(13)² =(12)² + (r)²
⇒ (r)² = 169 - 144
⇒ r =√25
⇒ r = 5cm
Hence, length of the radius of the cone is equals to 5 cm.
Learn more about right circular cone here
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