Volume and Surface Area of Solid Figures


  1. The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 60 cm). ?









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    Let the sides of the base are 5k, 12k and 13k, respectively.
    Given, perimeter of base = 60 cm
    ⇒ 5k + 12k + 13k = 60

    Correct Option: A

    Let the sides of the base are 5k, 12k and 13k, respectively.
    Given, perimeter of base = 60 cm
    ⇒ 5k + 12k + 13k = 60
    ∴ k = 60/30 = 2
    The sides of base are 10 cm, 24 cm 26 cm.
    ∴ Volume of prism = (1/2) x 10 x 24 x 50 = 6000 cm3


  1. A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid ?









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    Volume of the prism = (Area of the base ) x (Height)
    Volume of the pyramid = 1/3 (Area of the base ) x (Height)

    Correct Option: C

    Volume of the prism = (Area of the base ) x (Height)
    Volume of the pyramid = 1/3 (Area of the base ) x (Height)
    Required ratio = [A x H] / [(1/3) x A x H]
    Therefore, Ratio of the volumes of the prism and the pyramid = 3 : 1.



  1. The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surface of the cylinder to that of the cone is ?









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    Ratio of curved surface area of cylinder and cone = [2πrh] / [πr√h2 + r2]

    Correct Option: C

    Ratio of curved surface area of cylinder and cone = [2πrh] / [πr√h2 + r2]
    = [2 x 6 x 8] / [6 x √62 + 82]
    = 96/(6 x 10) = 96/60 = 8/5 = 8 : 5


  1. A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is ?









  1. View Hint View Answer Discuss in Forum

    Let required number of coins be n, Then,
    n x 1/3 x π (1/10)2 x 1 = π x (3)2 x 5

    Correct Option: B

    Let required number of coins be n, Then,
    n x 1/3 x π (1/10)2 x 1 = π x (3)2 x 5
    ∴ n = 9 x 5 x 3 x 100 = 13500



  1. How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each bullet being 4 cm in diameter ?









  1. View Hint View Answer Discuss in Forum

    Volume of 1 bullet = 4/3π(2)3 = (32/3 x 22/7) cm3
    Volume of the cube = (44)3

    Correct Option: B

    Volume of 1 bullet = 4/3π(2)3 = (32/3 x 22/7) cm3
    Volume of the cube = (44)3
    ∴ Number of bullets = Volume of solid/Volume of 1 bullet
    = (44)3 x 3 x 7 / 32 x 22 = 2541