A cone has a slant height of 8 cm and a radius of 2 cm. Estimate the surface area using π =3, and then calculate a more accurate surface area using π =3.14.

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initial estimate: 60 cm²better estimate: 62.8 cm²

Step-by-step explanation:

The total surface area of a cone with radius r and slant height s is ...

  A = πr² +πrs = πr(r +s)

For the given dimensions and π≈3, the area is approximately ...

  3(2 cm)(2 cm +8 cm) = 60 cm²

For π≈3.14, the area is approximately ...

  (20cm²)(3.14) = 62.8 cm²

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

7.666270253x10 raised to the 18th power