solid mensuration

Determine the area of the segment of a circle if the length of the chord is 15 inches & located 5 inches from the center of the circle.

  1. 👍
  2. 👎
  3. 👁
  1. Make your sketch
    let the radius be r
    r^2 = 5^2 + 7.5^2 = 81.25
    r - √81.25

    central angle formed by the chord:
    let Ø be the angle at the centre formed by the right-angled triangle

    tanØ = 5/7.5
    Ø = 33.69°
    central angle is 2Ø = 67.38°

    area of whole circle = π(√81.25)^2 = 81.25π

    so by simple ratio:
    area of sector:
    sector/84=1.25π = 67.38/360
    sector = ....

    area of triangle formed by the chord in that sector
    = (1/2)(15)(5) = 75/2

    area of segment = 75/2 - area of sector

    I will leave the button pushing up to you

    1. 👍
    2. 👎
  2. 42.35

    1. 👍
    2. 👎
  3. 89

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Solid Mensuration

    A circle having an area of 452 square inches is cut into two segments by a chord, which is 6 inches from the center of the circle. Find the area of the bigger segment.

  2. Geometry

    A circle is divided into two parts by a chord, 3cm a wat from the center. Find the area of the smaller part if the circle has an area of 201cm squared.

  3. calculus

    P /|\ / | \ / | \ on this side there is an / | \ arc with A(θ) in the / | \ middle. the B(θ) /θ | B(θ)\ triangle is not equal O -------------- R to the θ triangle. Q the figure shows a setor of a circle with central angle

  4. MATH

    1. The circle graph represents a family’s monthly budget. If the total monthly budget is $5,000, how much does the family spend on items other than food and housing? circle graph (1 point) $1,000$1,500$3,500$2,500 The following

  1. Math

    In the diagram, AE¯¯¯¯¯¯¯¯ is tangent to the circle at point A, and secant DE¯¯¯¯¯¯¯¯ intersects the circle at points C and D. The lines intersect outside the circle at point E. A circle with no center shown.

  2. maths

    a 4 cm long chord subtends a central angle of 60° . the radial segment of this circle is

  3. PleaseHelp! Geometry!

    Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

  4. mATH

    MY ANSWER RECORDED BELOW 1. The circle graph represents a family’s monthly budget. If the total monthly budget is $5,000, how much does the family spend on items other than food and housing? circle graph (1 point)

  1. pre-calculus

    find the area of the segment formed by a chord 24 cm long in a circle of radius 13 cm.

  2. Math

    A circle has a radius of 10 cm. A chord is 6 cm from the center. What is the length, in centimeters, of the chord?

  3. geometry

    Two secant segments are drawn to a circle from a point outside the circle. The external segment of the first secant segment is 8 centimeters and its internal segment is 6 centimeters. If the entire length of the second secant

  4. mathematics

    A Square ABCD inscribed in a circle of radius 4cm. What is the minor segment cut off by the chord AB

You can view more similar questions or ask a new question.