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Mathematics

The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.

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Answer

By formula,

Curved surface area = πrl

∴12320=227×56×l⇒l=12320×722×56⇒l=862401232=70.\therefore 12320 = \dfrac{22}{7} \times 56 \times l \\[1em] \Rightarrow l = \dfrac{12320 \times 7}{22 \times 56} \\[1em] \Rightarrow l = \dfrac{86240}{1232} = 70.

We know that,

⇒ l2 = h2 + r2

⇒ 702 = h2 + 562

⇒ 4900 = h2 + 3136

⇒ h2 = 4900 - 3136

⇒ h2 = 1764

⇒ h = 1764\sqrt{1764} = 42 cm.

Hence, height of cone = 42 cm.

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