Mensuration One Mark Online Test — Class 10 Mathematics

Mensuration One Mark Online Test (10th Standard Mathematics)

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The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

A.60\\(\pi\) \\(\text{ cm}^2\) B.68\\(\pi\) \\(\text{ cm}^2\) C.120\\(\pi\) \\(\text{ cm}^2\) D.136\\(\pi\) \\(\text{ cm}^2\)

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

A.4\\(\pi r^2\) \\(\text{ sq. units}\) B.6\\(\pi r^2\) \\(\text{ sq. units}\) C.3\\(\pi r^2\) \\(\text{ sq. units}\) D.8\\(\pi r^2\) \\(\text{ sq. units}\)

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

A.12 \\(\text{ cm}\) B.10 \\(\text{ cm}\) C.13 \\(\text{ cm}\) D.5 \\(\text{ cm}\)

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

A.1:2 B.1:4 C.1:6 D.1:8

The total surface area of a cylinder whose radius is \\(\frac{1}{3}\) of its height is

A.\\(\frac{9}{8}\)\\(\pi h^2\) \\(\text{ sq. units}\) B.24\\(\pi h^2\) \\(\text{ sq. units}\) C.\\(\frac{8}{9}\)\\(\pi h^2\) \\(\text{ sq. units}\) D.\\(\frac{56}{9}\)\\(\pi h^2\) \\(\text{ sq. units}\)

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

A.5600\\(\pi\) \\(\text{ cm}^3\) B.1120\\(\pi\) \\(\text{ cm}^3\) C.56\\(\pi\) \\(\text{ cm}^3\) D.3600\\(\pi\) \\(\text{ cm}^3\)

If the radius of the base of a cone is tripled and the height is doubled then the volume is

A.made 6 times B.made 18 times C.made 12 times D.unchanged

The total surface area of a hemi-sphere is how much times the square of its radius.

A.\\(\pi\) B.4\\(\pi\) C.3\\(\pi\) D.2\\(\pi\)

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

A.3x \\(\text{ cm}\) B.x \\(\text{ cm}\) C.4x \\(\text{ cm}\) D.2x \\(\text{ cm}\)

Q10

A frustum of a right circular cone is of height 16cm with radii of its ends as 8cm and 20cm. Then, the volume of the frustum is

A.3328\\(\pi\) \\(\text{ cm}^3\) B.3228\\(\pi\) \\(\text{ cm}^3\) C.3240\\(\pi\) \\(\text{ cm}^3\) D.3340\\(\pi\) \\(\text{ cm}^3\)

Q11

A shuttle cock used for playing badminton has the shape of the combination of

A.a cylinder and a sphere B.a hemisphere and a cone C.a sphere and a cone D.frustum of a cone and a hemisphere

Q12

A spherical ball of radius \(r_1\) units is melted to make 8 new identical balls each of radius \(r_2\) units. Then \(r_1 : r_2\) is

A.2:1 B.1:2 C.4:1 D.1:4

Q13

The volume (in \\(\text{cm}^3\)) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

A.\\(\frac{4}{3}\)\\(\pi\) B.\\(\frac{10}{3}\)\\(\pi\) C.5\\(\pi\) D.\\(\frac{20}{3}\)\\(\pi\)

Q14

The height and radius of the cone of which the frustum is a part are \(h_1\) units and \(r_1\) units respectively. Height of the frustum is \(h_2\) units and radius of the smaller base is \(r_2\) units. If \(h_2 : h_1 = 1 : 2\) then \(r_2 : r_1\) is

A.1:3 B.1:2 C.2:1 D.3:1

Q15

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

A.1:2:3 B.2:1:3 C.1:3:2 D.3:1:2

Q16

If the radius of a right circular cylinder is doubled and its height is halved, how does its curved surface area change?

A.It is halved B.It remains unchanged C.It is doubled D.It is quadrupled

Q17

What is the curved surface area of a solid right circular cone whose base radius is \(7\text{ cm}\) and height is \(24\text{ cm}\)?

A.\(168\pi\text{ cm}^2\) B.\(175\pi\text{ cm}^2\) C.\(185\pi\text{ cm}^2\) D.\(576\pi\text{ cm}^2\)

Q18

If the numerical value of the volume of a solid hemisphere is equal to its total surface area, then what is its radius?

A.\(2\text{ units}\) B.\(3\text{ units}\) C.\(4.5\text{ units}\) D.\(9\text{ units}\)

Q19

If the ratio of the surface areas of two spheres is \(4:9\), then what is the ratio of their volumes?

A.2:3 B.4:9 C.8:27 D.16:81

Q20

The volume of a right circular cylinder is \(360\pi\text{ cm}^3\). If its height is \(10\text{ cm}\), what is its curved surface area?

A.\(60\pi\text{ cm}^2\) B.\(72\pi\text{ cm}^2\) C.\(120\pi\text{ cm}^2\) D.\(240\pi\text{ cm}^2\)

Q21

If a right circular cylinder and a cone have the same base radius and the same height, and the volume of the cylinder is \(120\text{ cm}^3\), then what is the volume of the cone?

A.\(40\text{ cm}^3\) B.\(60\text{ cm}^3\) C.\(240\text{ cm}^3\) D.\(360\text{ cm}^3\)

Q22

The outer and inner radii of a right circular hollow cylinder are \(5\text{ cm}\) and \(3\text{ cm}\) respectively, and its height is \(10\text{ cm}\). Find its total surface area.

A.\(160\pi\text{ cm}^2\) B.\(176\pi\text{ cm}^2\) C.\(192\pi\text{ cm}^2\) D.\(224\pi\text{ cm}^2\)

Q23

A frustum of a cone has a height of \(4\text{ cm}\). If the radii of its circular bases are \(6\text{ cm}\) and \(3\text{ cm}\), what is its slant height?

A.\(3\text{ cm}\) B.\(4\text{ cm}\) C.\(5\text{ cm}\) D.\(7\text{ cm}\)

Q24

A solid metallic sphere of radius \(6\text{ cm}\) is melted and recast into a solid cylinder of radius \(8\text{ cm}\). What is the height of the cylinder?

A.\(3.5\text{ cm}\) B.\(4.5\text{ cm}\) C.\(6\text{ cm}\) D.\(9\text{ cm}\)

Q25

If the radius of a sphere is doubled, then its surface area increases by what percentage?

A.100\% B.200\% C.300\% D.400\%

Q26

A solid cone has a base radius of \(5\text{ cm}\) and a slant height of \(13\text{ cm}\). What is its total surface area?

A.\(65\pi\text{ cm}^2\) B.\(90\pi\text{ cm}^2\) C.\(120\pi\text{ cm}^2\) D.\(180\pi\text{ cm}^2\)

Q27

What is the ratio of the curved surface area to the total surface area of a solid hemisphere?

A.1:2 B.2:3 C.3:4 D.2:1

Q28

A sphere of radius \(r\) is inscribed inside a right circular cylinder of radius \(r\) and height \(2r\). What is the ratio of the volume of the cylinder to the volume of the sphere?

A.1:1 B.3:2 C.4:3 D.2:3

Q29

If the volume of a sphere is \(\frac{32}{3}\pi\text{ cm}^3\), then what is its surface area?

A.\(8\pi\text{ cm}^2\) B.\(12\pi\text{ cm}^2\) C.\(16\pi\text{ cm}^2\) D.\(32\pi\text{ cm}^2\)

Q30

A toy is formed by surmounting a cone of height \(4\text{ cm}\) on a solid hemisphere of radius \(3\text{ cm}\). Find the total volume of the toy.

A.\(18\pi\text{ cm}^3\) B.\(24\pi\text{ cm}^3\) C.\(30\pi\text{ cm}^3\) D.\(36\pi\text{ cm}^3\)

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About this Mensuration test

This free online practice test covers Mensuration from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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