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Mensuration Test 7
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Mensuration Test 7
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  • Question 1/10
    1 / -0

    The edges of a cuboid are in the ratio 3:4:5 and its surface area is 188 sq.cm. The volume of the cuboid is.

    Solutions

    Explanation : sides 3x,4x,5x

    Surface area = 188

    2(lb+bh+hl)=188

    X^2 = 94/47

    X=1.41

    Volume= l*b*h= 168.19 cubic cm

     

  • Question 2/10
    1 / -0

    A solid metallic cone of height 20cm radius of base 30 cm is melted to make spherical balls each of 10cm diameter. How many such balls can be made?

    Solutions

    Explanation :

    Exp: n*4/3 * π r^3 = ⅓ π * R^2 *h

    n= 36

     

  • Question 3/10
    1 / -0

    The length and breadth of a rectangle are increased by 32% and 25% respectively. Its area will be increased by.

    Solutions

    Explanation :32 + 25 + (32*25/100)

     

  • Question 4/10
    1 / -0

    A right triangle with sides 15,16 and 18cm is rotated about the side 15cm to form a cone. The volume of the cone will be.

    Solutions

    Explanation :

    h= 15, r = 16

    Volume= ⅓ * π * (16)^2 * 15

     

  • Question 5/10
    1 / -0

    After measuring 320m of a rope, it was discovered that the measuring metre rod was 6cm longer. The true length of the rope measured is.

    Solutions

    Explanation :

    True length= 320m + 320* 3cm

    320m + 960cm

    329m 60cm(1m=100cm)

     

  • Question 6/10
    1 / -0

    If the height and the radius of the base of a cone are each increased by 100%, then the volume of the cone becomes.

    Solutions

    Explanation :

    Diameter of semi-circumference= r

    New height=h+h=2h

    New radius=r+r= 2r

    Volume= ⅓ π* r^2 h

    New volume= ⅓ π (2r)^2 * 2h

    New/original = 8/1

     

  • Question 7/10
    1 / -0

    The perimeter of a rhombus is 300cm. If one of its diagonals is 16cm then the area of the rhombus is

    Solutions

     

    Explanation :

    Length of one side of rhombus= 300/4=75cm

    Other diagonal= 2 * root of (75)^2 – 8^2

    = 149

    Area= ½ * 16 * 149

     

  • Question 8/10
    1 / -0

    The height of a cone is 60cm. A small cone is cut off at the top of by a plane parallel to its base. If its volume is 1/64 of volume of the cone, at what height above the base is the section made?

    Solutions

    Explanation :

    (⅓ * π * r1^2 * h1 )/ (⅓ π * r^2 * h) / 1/64

    (r1/r)^2 * h1/h = 1/64

    (h1/h) ^3 = (¼)^3 ( r1/r = h1/h)

    h1 = ¼ * 60=15

     

  • Question 9/10
    1 / -0

    Volume of a cube whose diagonal measures 36*root3 cm?

    Solutions

    Explanation :

    Diagonal= root 3 * side

    Side =36

    Volume= 36^3

     

  • Question 10/10
    1 / -0

    A wire when bent in the form of a square enclose an area of 841 sq cm. What will be enclosed area when the samd wire is bent into the form of a circle?

    Solutions

    Explanation :

    area of square= side^2

    Side = root 841 = 29

    Perimeter= 4*29 = 116cm

    According to question circle is made by same wire so

    Perimeter if square= circumference of circle

    116= 2πr

    r=18.45

     

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