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WAEC 2021 · Paper 2 · Q3

The curved surface area of a cone is 242 cm2242\text{ cm}^2. If the slant height is 4 cm4\text{ cm} more than the radius, calculate, correct to one decimal place, the: [Take π=227]\left[\text{Take }\pi = \frac{22}{7}\right]

  1. (a)

    radius;

  2. (b)

    height;

  3. (c)

    volume of the cone.

Worked solution (try it first)

(a)

  1. Let the radius be rr.
  2. Then l=r+4l = r + 4.
  3. Curved surface: 227×r(r+4)=242\frac{22}{7} \times r(r + 4) = 242, so r2+4r=77r^2 + 4r = 77 and r2+4r−77=0r^2 + 4r - 77 = 0.
  4. Factorise: (r+11)(r−7)=0(r + 11)(r - 7) = 0.
  5. The radius is positive, so r=7.0r = 7.0 cm.

(b)

  1. l=11l = 11 cm, so h=112−72h = \sqrt{11^2 - 7^2}
    =72= \sqrt{72}
    ≈8.5\approx 8.5 cm.

(c)

  1. Volume =13×227×72×72= \frac13 \times \frac{22}{7} \times 7^2 \times \sqrt{72}
    ≈435.6 cm3\approx 435.6\text{ cm}^3.

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