A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it? (Please explain and show work)

  (47/48)*pi*r^2*h

Work Shown:

A = volume of the cylinder

A = pi*(radius)^2*(height)

A = pi*r^2*h

The cone's base has diameter r/2, so its radius is (1/2)*(r/2) = r/4

B = volume of the cone

B = (1/3)*(volume of cylinder with radius r/4 and height h)

B = (1/3)pi*(r/4)^2*h

B = (1/3)*pi*(r^2)/(4^2)*h

B = (1/3)*pi*(r^2)/16*h

B = (1/3)*(1/16)*pi*r^2*h

B = (1/48)pi*r^2*h

B = (1/48)*A

B = (1/48)*(volume of cylinder)

C = volume of the empty space/air inside cylinder, but outside cone

C = A-B

C = A - (1/48)*A

C = (48/48)A - (1/48)A

C = (48A)/48 - (A/48)

C = (48A-A)/48

C = 47A/48

C = (47/48)*A

C = (47/48)*pi*r^2*h

Sorry can't answer that question

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12