Mensuration · SSC CGL previous year questions

A vertical cylindrical container is filled with oil. A solid hemispherical stone of radius 7 cm is immersed completely, and the oil level rises by 3 cm. What is the radius of the cylinder?

1. A.6.29 cm
2. B.7.43 cm
3. C.8.73 cm
4. D.11.41 cm

$△$ABC is a right-angled triangle with $\angle ABC=90^{\circ }$. If AB = 28 cm, and BC = 96 cm, find the area (in cm${}^2$) of the circumcircle of $△$ABC. (Use $\pi$ = 3.14.)

1. A.7,536
2. B.7,693
3. C.8,164
4. D.7,850

What is the total surface area of a cone whose curved surface area is 550 cm² and radius is 7 cm? (Take π = 22/7)

1. A.704.00 cm²
2. B.714.05 cm²
3. C.682.60 cm²
4. D.764.71 cm²

If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of the cylinder is (use π = 22 / 7):

1. A.3432 cm²
2. B.5212 cm²
3. C.3816 cm²
4. D.4312 cm²

The central angle of a sector is 80° and whose length is 96π. What is the radius of the circle?

1. A.196 units
2. B.216 units
3. C.204 units
4. D.116 units

In a circle with center O, an arc ABC subtends an angle of 138° at the centre of the circle. The chord AB is produced to a point P. Then, the measure of ∠CBP is:

1. A.42°
2. B.111°
3. C.69°
4. D.108°

Find the volume of a cone having base radius 3.5 cm and height 18 cm.

1. A.221 cm³
2. B.241 cm³
3. C.201 cm³
4. D.231 cm³

A secant PAB is drawn from an external point P to the circle with the centre at O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:

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

The centres of two circles are 36 cm apart. If the radii of these two circles are 15 cm and 9 cm, respectively, then what is the sum of the lengths (in cm) of a direct common tangent and a transverse common tangent of these two circles?

1. A.6√7(√7 + 2)
2. B.6√5(√5 + 2)
3. C.6√7(√5 + 2)
4. D.6√5(√7 + 2)

It is always possible to draw a circle passing through ______ non-collinear points in a plane.

1. A.3
2. B.6
3. C.5
4. D.4

A circular arc whose radius is 14 cm, makes an angle of 45° at the centre. Find the perimeter (in cm) of the sector. (Use )

1. A.38
2. B.39
3. C.34
4. D.28

The two circles intersect at two points P and Q. PR and PS are diameters of the two circles. What is ∠PQR?

1. A.45°
2. B.0°
3. C.90°
4. D.60°

Find the diameter (in cm) of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 12 cm and 16 cm.

1. A.28
2. B.32
3. C.64
4. D.56

'x' varies directly with the cube of 'y', and inversely with the square of 'z'. If $x=\frac{1}{36}$ when y = 2 and z = 3, then what is the value of 800x when y = 3 and z = 5?

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

A well with 14 cm radius is dug 23 cm deep. Find the volume of the earth taken out of it.

1. A.14,168 cm³
2. B.14,108 cm³
3. C.15,168 cm³
4. D.14,178 cm³

In the figure shown above, quadrilateral PQRS has its vertices on the circumference of the circle with centre O. If m ∠QOS = 20x° and m ∠QRS = 26x°, then what is the value of ‘x’?

1. A.4
2. B.3
3. C.6
4. D.5

From a point T, a tangent TP at point P, is drawn to a circle with center O. A secant TQR (point Q is near to point T) is drawn from the point T. ∆PQR is inscribed into the circle by joining the points P, Q, and R. Draw lines OQ and OR. If ∠PTQ is 27° and ∠TPQ = 55°, what is the degree measure of ∠ROQ?

1. A.94
2. B.86
3. C.98
4. D.82

PQ is the diameter of a circle with centre A. M is a point on the circumference of the circle. If m ∠MAP = 110°, then find the value of m ∠MQA.

1. A.70°
2. B.55°
3. C.35°
4. D.65°

The volume of a right circular cylindrical box of radius 30 cm is 600 cm3 . Find the height of the box.

1. A.0.21 cm
2. B.0.61 cm
3. C.0.51 cm
4. D.0.31 cm

What is the length (in cm) of each side of a cube if the volume of a cube is 13,824 cm³?

1. A.20.4
2. B.24
3. C.34
4. D.22

The radii of two concentric circles are 26 cm and 10 cm. If the chord of the greater circle is a tangent to the smaller circle, then find the length of that chord.

1. A.48 cm
2. B.28 cm
3. C.38.7 cm
4. D.28.7 cm

The radii of two circles are 8 cm and 15 cm. The perimeter of the circle having area equal to the sum of the areas of the two circles (in cm) is:

1. A.32π
2. B.34π
3. C.28π
4. D.30π

Let C be a circle with centre O and PQ be a minor arc on C. Let R and S be two points on the major arc of PQ on C. If PQ subtends an angle 80° at O, find ∠PRQ and ∠PSQ, respectively.

1. A.40° and 50°
2. B.50° and 80°
3. C.40° and 60°
4. D.40° and 40°

A line cuts two concentric circles. The length of chords formed by this line on the circles is 6 cm and 18 cm. Find the difference in the squares of the radii of two circles.

1. A.72
2. B.90
3. C.120
4. D.60

For two circles of radius 7 units and $\frac{7}{2}$ units, whose centres are 15 units apart, what is the length of the direct common tangent in units? (Correct to 3 decimal places.)

1. A.14.586
2. B.18.654
3. C.16.584
4. D.15.486