10th Class Mathematics Surface Areas and Volumes Question Bank Surface Area and Volume (Mensuration)

  • question_answer A spherical metal ball of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by n%. Then n =?

    A)  900   

    B)  800          

    C)  600                             

    D)  200

    Correct Answer: A

    Solution :

    (a): Let radius of a smaller sphere be ?r cm?. \[\frac{4}{3}\times \pi \times {{(10)}^{3}}=1000\times \frac{4}{3}\times \pi \times {{(r)}^{3}}\] \[r=1\,\,cm\] Surface area of the larger sphere \[=4\pi {{(10)}^{2}}\]                                                 \[=400\pi \] Total surface area of 1000 smaller spheres \[=1000\times 4\pi {{(1)}^{2}}=4000\pi \] Increase in the surface area \[=4000\pi -400\pi \]                                         \[=3600\pi \] Hence, surface area of the metal is increased by 900%. Therefore n = 900.                           


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