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SSC CGL level Question Set 41, Mensuration 3

41st SSC CGL level Question Set, 3rd on topic Mensuration

SSC CGL question set 41 mensuration-3

This is the 41st question set of 10 practice problem exercise for SSC CGL exam and 3rd on topic Mensuration. Students should complete this question set in prescribed time first and then only refer to the corresponding solution set.

We will repeat here the method of taking a 10 problem test if you have not gone through it already.

Method for taking this 10 problem test and get the best results from the test set:

  1. Before start, go through the tutorials Basic concepts on Geometry 1, Basic concepts on Geometry 2, Basic concepts on Geometry 3 or any other short but good material to refresh your concepts if you so require.
  2. Answer the questions in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.
  3. When the time limit of 15 minutes is over, mark up to which you have answered, but go on to complete the set.
  4. At the end, refer to the answers at the end of this question set to mark your score at 15 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.
  5. Identify and analyze the problems that you couldn't do to learn how to solve those problems.
  6. Identify and analyze the problems that you solved incorrectly. Identify the reasons behind the errors. If it is because of your shortcoming in topic knowledge improve it by referring to only that part of concept from the best source you get hold of. You might google it. If it is because of your method of answering, analyze and improve those aspects specifically.
  7. Identify and analyze the problems that posed difficulties for you and delayed you. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.
  8. Give a gap before you take a 10 problem practice test again.

Important: both practice tests and mock tests must be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.

Resources that should be useful for you

You may refer to:

7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests or section on SSC CGL to access all the valuable student resources that we have created specifically for SSC CGL, but generally for any hard MCQ test.

Tutorials that you should refer to

Basic concepts on Geometry 1 lines points and triangles

Basic concepts on Geometry 2 quadrilaterals polygons squares

Basic and rich concepts on Geometry 3 Circles

Basic and rich Geometry concepts part 4 Arc angle subtending concept proof

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41st question set - 10 problems for SSC CGL exam: topic Mensuration - Answering time 15 mins

Problem 1.

If in $\triangle ABC$, D and E are the two points on the sides AB and AC respectively so that DE || BC and $\displaystyle\frac{AD}{BD}=\displaystyle\frac{2}{3}$, then $\displaystyle\frac{\text{The area of trapezium DECB}}{\text{The area of }\triangle ABC}$ is equal to,

  1. $\displaystyle\frac{21}{25}$
  2. $\displaystyle\frac{5}{9}$
  3. $5\displaystyle\frac{1}{4}$
  4. $1\displaystyle\frac{4}{5}$

Problem 2.

A solid cone of height 9cm with diameter of its base 18cm is cut out from a wooden solid sphere of radius 9cm. The percentage of wood wasted is,

  1. 50%
  2. 75%
  3. 25%
  4. 30%

Problem 3.

Two circles with centres A and B and radius 2cm touch each other externally at C. A third circle with centre at C and radius 2cm meets the other two at D and E on the same side of the line AB joining the two centres. Then the area of the quadrilateral ABED is,

  1. $2\sqrt{2}$ sq cm.
  2. $3\sqrt{2}$ sq cm
  3. $2\sqrt{3}$ sq cm
  4. $3\sqrt{3}$ sq cm

Problem 4.

At each corner of a triangular field of side lengths 26m, 28m and 30m, a cow is tethered by a rope of length 7m. The area (in sq m) ungrazed by the cows is,

  1. 336
  2. 77
  3. 259
  4. 154

Problem 5.

ABC is an equilateral triangle of side 2cm. With A, B, C as centre and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is,

  1. $\left(\displaystyle\frac{\pi}{2} - \sqrt{3}\right)$ sq cm
  2. $\left(\sqrt{3} - \displaystyle\frac{\pi}{2}\right)$ sq cm
  3. $\left(\sqrt{3} - \displaystyle\frac{3\pi}{2}\right)$ sq cm
  4. $3\left(3\sqrt{3} - \displaystyle\frac{\pi}{2}\right)$ sq cm

Problem 6.

If the length of each side of a regular tetrahedron is 12cm, then the volume of the tetrahedron is,

  1. $144\sqrt{2}$ cm$^3$
  2. $12\sqrt{2}$ cm$^3$
  3. $72\sqrt{2}$ cm$^3$
  4. $8\sqrt{2}$ cm$^3$

Problem 7.

The surface area of three adjacent faces of a cuboid are, p, q and r. Its volume is,

  1. $\sqrt{pq^2 + qr^2 + rp^2}$
  2. $\sqrt{(p^2+q^2+r^2)(p+q+r)}$
  3. $\sqrt{pqr}$
  4. $(\sqrt{pq}+\sqrt{qr}+\sqrt{rp})(p^2+q^2+r^2)$

Problem 8.

The radii of the base of a cylinder and a cone are in the ratio $\sqrt{3}:\sqrt{2}$ and their heights are in the ratio of $\sqrt{2}:\sqrt{3}$. Their volumes are in the ratio of,

  1. $\sqrt{2}:\sqrt{6}$
  2. $\sqrt{3}:2\sqrt{2}$
  3. $3\sqrt{3}:\sqrt{2}$
  4. $\sqrt{3}:\sqrt{2}$

Problem 9.

The height of a cone is 30cm. A small cone is cut-off at the top by a plane parallel to its base. If its volume is $\displaystyle\frac{1}{27}$th of the volume of the cone, at what height above the base is the section made?

  1. 10cm
  2. 6cm
  3. 8cm
  4. 20cm

Problem 10.

The radius of a cylinder is 10cm and height is 4cm. The number of centimetres that may be added either to the radius or to the height to get the same increase in volume is,

  1. 5cm
  2. 4cm
  3. 25cm
  4. 16cm

Answer to the questions

Problem 1. Ans. Option a: $\displaystyle\frac{21}{25}$.

Problem 2. Ans. Option b : 75%.

Problem 3. Ans. Option d: $3\sqrt{3}$ sq cm.

Problem 4. Ans. Option c: 259 sq m.

Problem 5. Ans. Option b: $\left(\sqrt{3} - \displaystyle\frac{\pi}{2}\right)$ sq cm.

Problem 6. Ans. Option a : $144\sqrt{2}$ cm$^3$.

Problem 7. Ans. Option c$\sqrt{pqr}$.

Problem 8. Ans. Option c: $3\sqrt{3} : \sqrt{2}$.

Problem 9. Ans. Option d: 20cm.

Problem 10. Ans. Option a: 5cm.


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