Miscellaneous Mensuration (Simple) | Learn Mathematics Online

Miscellaneous Mensuration (Simple)

Study Material (PDF)

Study Material (PDF)

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Question No: #151

The curved surface area of a right-circular cone and a cylinder are equal. If the height and radius of the cone are `h` and `r` respectively and the height and radius of the cylinder is `H` and `r` respectively. Then show that, `h^2 = (2H+r)(2H-r)`.

Ans:

Question No: #152

The height and slant height of a solid right-circular cone are 20 cm and 25 cm respectively. If a solid right-circular cylinder has a same volume of the cone and height of the cylinder is 15 cm, then calculate the diameter of cylinder.

Ans: 20 cm

Question No: #153

Fill in the blanks.
(i) If a solid sphere is melted to form a solid right-circular cylinder, then the sphere and cylinder will have the same ......... .
(ii) The shape of a pencil cutting one face is a combination of cone and .......... .

Ans: (i) volume (আয়তন), (ii) cylinder (চোঙ)

Question No: #154

The length and radius of base of a right-circular cylinder are `h` and `r` respectively. If its volume is equal to the volume of a sphere of equal radius, then the relationship between `h` and `r` is ......... .

Ans: `3h=4r`

Question No: #155

If a sphere is made by melting a solid right circular cylinder of radus `2x` cm and height `x` cm, then the radius of the sphere will be ........ cm.

Ans: $ x\sqrt[3]{3} $

Question No: #156

A solid metal rod of height 8 cm is melted to form a solid sphere of equal radius. But find the diameter of the sphere.

Ans:

Question No: #157

The radius of cross-section of a right circular rod is 3.2 dcm. The rod is melted to make 21 solid spheres. If the radius of each sphere be 8 cm, then what will be the length of the rod?

Ans: 14 cm

Question No: #158

The radius of base of a solid right circular iron-rod is 32 cm and the length of the rod is 35 cm. How many solid right circular cone of radius of base 8 cm and height 28 cm can be made by melting this rod?

Ans: 60

Question No: #159

The length, breadth and height of a solid rectangular parallelepiped are 11 cm, 9 cm and 6 cm respectively. How many coins of diameter 3 cm and thickness `1/4` cm can be made from this rectangular parallelepiped?

Ans: 336

Question No: #160

Determine the length of a right circular rod of 2.8 cm diameter made by the casting a solid gold sphere of 4.2 cm radius.

Ans: 50.4 cm