Question

the radius and height of a cone are in the ratio 4:3 the area of basre is 154 cm find the areaof curved surface

Answer 1

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Good Question and Keep Progressing.

Here is your answer---

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Let the radius and Height of the cone be 4x and 3x respectively.

Given---
  Area of the Base of the cone = 154 cm^2
                      pie × r^2 = 154
                 (22/7) × r^2 = 154
                          (4x)^2 = 154 × (7/22)
                          16 x^2 = 49
                               x^2 =49/16
                                   x = √(49/16)
                                   x = 7/4

Thus, Radius = 4x
                      = 4 × (7/4)
                      = 7 cm.
           
          Height = 3x
                      = 3 × (7/4)
                      = 21/4 cm.


For the Slant Height(l),
     Using the Formula,
                          (l)^2 = (r)^2 + (h)^2
                          (l)^2 = (7)^2 + (21/4)^2
                          (l)^2 = 49 + 27.5625
                          (l)^2  = 76.5625
                             l = √76.5625
                             l = 8.75

Using the Formula,
           Curved Surface Area = pie × r × l
                                              = (22/7) × 27 × 8.75
                                              = 742.5 cm^2.



Thus, Curved Surface Area of the CONE is 742.5 cm^2.

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Hope it helps.

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Have a nice day.

Answer 2

Answer:

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