Question

Please solve Q. 4, 5, 7, and 11 given in the picture.
Ans.-
4. 1848cm^2
5. 27309+1/3 cm^3
7. 1257+ 1/7 cm^2
11. 101+ 2/21 cm^3

Answer 1

Q 4.
   Radii of spheres = R1 and  R2 = 7 cm
    Volumes of spheres
           V1 = 4π/3 *R1³,        V2 = 4π/3 * 7³ cm³
      Given     V1 - V2 = 10,061  1/3  cm³  = 30184/3 cm³
       So      V1 = 30184/3 +  4π*7³ /3  cm³ = 34496/3 cm^3
         R1³ = 34496/3 * 3/4π = 2744 cm^3 
        R1 = 14 cm
================

Q5 . 
      Surface areas :  4 π 21² cm²  and  4 π R2²
      Difference:    4 π (21² - R2²) = 3,080 cm²    given
      21²  - R2² = 3080 * 7/88
          R2² = 195.76
           R2 = 14 cm  nearly
     Difference in volumes:     4 π /3 *  (21³ - 14³) = 81928/3 cm³
                   = 27309  1/3  cm³

===========

Q7.  
  R cm = outer radius of shell.
  Inner diameter = 16 cm .   inner radius = 8 cm.

  Volume of the shell = 4π/3 * [ R³ - 8³]  cm³        Outer volume minus inner volume

   given  4π/3 * [ R³ - 8³ ] =   2,044  20/21  = (2044*21+20)/21  cm³
         R^3 - 8³ = 488 
         So R = 10 cm
       
Outer surface area =  4 π R² = 8800/7  cm²

=========
Q11.

Quantity of metal to make the cup = volume of the material.
          = volume of outer hemisphere  -   volume of inner hemisphere.
      
Capacity of the cup = volume of inner hemisphere = 89  5/6 cm^3  = 539/6 cm^3
Inner radius = R1
volume of hemisphere = 2π/3 R1³ = 539/6
              R1 = 3.50 cm
     Given thickness of the cup = 1 cm
Outer radius of the cup = R2 = 3.50 + 1 = 4.50 cm
Outer volume = 2π/3 * R2³ = 190.92 cm^3

Difference of the two volumes=  101.09 cm³
 .... calculate in whole numbers and fractions instead of decimals.