Question 1

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

Accepted Answer

Area of the park = (60 x 40) = 2400 sq.m Area of the lawn = 2109 sq.m Area of the crossroads = (2400 - 2109) = 291 sq.m Let the width of the road be x metres. Then, 60x + 40x - (x * x) = 291 =>(x * x) - 100x + 291 = 0 =>(x - 97)(x - 3) = 0 =>x=3

Question 2

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

Accepted Answer

Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m.

Question 3

A large cube is formed from the material obtained by melting three smaller cubes of 3,4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Accepted Answer

25 : 18

Question 4

What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter

Accepted Answer

Volume of cylinder / Volume of cone = 3/1

Question 5

If the base of a pyramid is a square of 6cm side and its slant height is 5cm. Find its slant surface area.

Accepted Answer

Slant surface of a pyramid=1/2 perimeter of base slantheight =1/2 x (4 x Side of squarebase) x Slantheight

Question 6

The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :

Accepted Answer

27:28

Question 7

A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

Accepted Answer

4.63 cm

Question 8

Three consecutive angles of a cycle quadrilateral are in the ratio of 1 : 4 : 5 . The measure of fourth angle is

Accepted Answer

60°

Question 9

In triangle ABC, ∠ABC = 15 deg. D is a point on BC such that AD = BD. What is the measure of ∠ADC (in degrees)?

Accepted Answer

30

Question 10

The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

Accepted Answer

7

Question 11

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

Accepted Answer

77

Question 12

In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

Accepted Answer

112.5

Question 13

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel. What is the area of triangle ADC?

Accepted Answer

126 SQ.CM

Question 14

In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

Accepted Answer

6√7 cm

Question 15

Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?

Accepted Answer

Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively. Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered) Hence in ΔABD, AD is a median ⇒ AB + AC > 2(AD) Similarly, we get BC + AC > 2CF BC + AB > 2BE On adding the above inequations, we get (AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE 2(AB + BC + AC) > 2(AD + BE + CF) ∴ AB + BC + AC > AD + BE +CF 2. To prove: AB + BC + CA > 2AD Construction: AD is joined Proof: In triangle ABD, AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the third side] ---- 1 In triangle ADC, AC + DC > AD [because, the sum of any two sides of a tri angle is always greater than the third side] ---- 2 Adding 1 and 2 we get, AB + BD + AC + DC > AD + AD => AB + (BD + DC) + AC > 2AD => AB + BC + AC > 2AD Hence proved

Question 16

What is the percentage decrease in the area of a triangle if its each side is halved?

Accepted Answer

Area of triangle of = ½*a*b* sinθ = A Where a and b are sides of the triangle and θ be the angle between them After decreasing each side New area = ½*(a/2)*(b/2)*sinθ = ¼ A %decrease = [(A–¼ A)/A ]*100 = 75%

Question 17

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

Accepted Answer

2 cm or 14 cm

Question 18

The co-ordinates of the centroid of a triangle ABC are (-1 , 4). What are the co-ordinates of vertex C if co-ordinates of A and B are (-3 , -1) and (3 , 5) respectively?

Accepted Answer

(-3 , 8)

Question 19

What is the reflection of the point (-4, 3) in the line x = -2?

Accepted Answer

(0 , 3)

Question 20

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

Accepted Answer

12

Volume and Surface Area Questions