## Questions on Mensuration for SSC CGL Set 41 with answers

Solve 10 questions on mensuration for SSC CGL Set 41 in 15 minutes. Verify your solutions from answers. Learn to solve the questions quickly from solutions.

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### 10 questions on mensuration for SSC CGL Set 41 - 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,

- $\displaystyle\frac{21}{25}$
- $\displaystyle\frac{5}{9}$
- $5\displaystyle\frac{1}{4}$
- $1\displaystyle\frac{4}{5}$

**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,

- 50%
- 75%
- 25%
- 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,

- $2\sqrt{2}$ sq cm.
- $3\sqrt{2}$ sq cm
- $2\sqrt{3}$ sq cm
- $3\sqrt{3}$ 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,

- 336
- 77
- 259
- 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,

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

**Problem 6.**

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

- $144\sqrt{2}$ cm$^3$
- $12\sqrt{2}$ cm$^3$
- $72\sqrt{2}$ cm$^3$
- $8\sqrt{2}$ cm$^3$

**Problem 7.**

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

- $\sqrt{pq^2 + qr^2 + rp^2}$
- $\sqrt{(p^2+q^2+r^2)(p+q+r)}$
- $\sqrt{pqr}$
- $(\sqrt{pq}+\sqrt{qr}+\sqrt{rp})(p^2+q^2+r^2)$

**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,

- $\sqrt{2}:\sqrt{6}$
- $\sqrt{3}:2\sqrt{2}$
- $3\sqrt{3}:\sqrt{2}$
- $\sqrt{3}:\sqrt{2}$

**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?

- 10cm
- 6cm
- 8cm
- 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,

- 5cm
- 4cm
- 25cm
- 16cm

Know how to solve the questions quickly at,

**Solution to Mensuration for SSC CGL Set 41.**

### Answers to the questions on mensuration for SSC CGL Set 41

**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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