NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.4 Solutions

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NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volume Exercise 13.4 Solutions are based on the following concepts:

  • Height of the cylinder based on given condition
  • Radius of the resulting sphere
  • Number of cones for a given situation.
  • Number of coins formed by melting a cuboid structured object.

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CBSE X Related Questions

1.

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

      2.

      The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :

      Length (in mm)

      Number of leaves

      118 - 126

      3

      127 - 135 

      5

      136 - 144

      9

      145 - 153

      12

      154 - 162

      5

      163 - 171

      4

      172 - 180

      2

      Find the median length of the leaves. 
      (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

          3.
          Find the sums given below :
          1. \(7 + 10\frac 12+ 14 + ....... + 84\)
          2. \(34 + 32 + 30 + ....... + 10\)
          3. \(–5 + (–8) + (–11) + ....... + (–230)\)

              4.
              A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

                  5.

                  A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

                      6.
                      A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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