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The volume of a right circular cone is 9856 cm^{3} and the area of its base is 616 cm^{2} .

Find the slant height of the cone.

Answer:

**Solution:**

Assume that a cone has a height of "h" and a circular base with radius "r." This cone will have a volume that is one-third of the product of the base's area and its height.

Given base area of the cone = 616 cm^{2}

π r^{2} = 616

(22/7)×r^{2} = 616

r^{2} = 616×7/22

r^{2} = 196

r = 14

Given volume of the cone = 9856 cm^{3}

(1/3)π r^{2}h = 9856

(1/3)×(22/7)×14^{2} ×h = 9856

h = (9856×3×7)/(22×14^{2})

h = (9856×3×7)/(22×196)

h = 48

Slant height, l = √(h^{2}+r^{2})

*l* = √(48^{2}+14^{2})

*l* = √(2304+196)

*l* = √(2500

*l* = 50

**Hence the slant height of the cone is 50 cm.**

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