#### Data Interpretation

• ( 1 ) The height of a cone is 60cm. A small cone is cut off at the top of by a plane parallel to its base. If its volume is 1/64 of volume of the cone, at what height above the base is the section made?

• 1) 17cm
• 2) 50m
• 3) 15m
• 4) 25m
• Discussion in forum
Solution : (1/3 * π * r12 * h1 )/ (1/3 π * r2 * h) / 1/64
(r1/r)2 * h1/h = 1/64
(h1/h)3 = (1/4)3 ( r1/r = h1/h)
h1 = (1/4) * 60 = 15

discussion

• ( 2 ) The width of a rectangle is 10 meter and its area is 120 square meter. If length of the rectangle is increased by 6.What is the new perimeter of the rectangle?

• 1) 65
• 2) 56
• 3) 85
• 4) 56
• Discussion in forum
Solution : Length = 120/10 = 12
(12 + 6) = 18
Perimeter = 2(10 + 18) = 56

discussion

• ( 3 ) There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.

• 1) 6π cm
• 2) 8π cm
• 3) 12π cm
• 4) 16π cm
• Discussion in forum
Solution : Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6
Circumference of the smaller circle = 2πs = 12π cm.

discussion

• ( 4 ) An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

• 1) Rs. 3642.40
• 2) Rs. 3868.80
• 3) Rs. 4216.20
• 4) Rs. 4082.40
• Discussion in forum
Solution : Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

discussion

• ( 5 ) The total cost of painting the walls of a room is Rs 475. Find the cost of painting the walls of another room whose length, breadth and height each are double than the dimensions of the previous room.

• 1) Rs 1780
• 2) Rs 1900
• 3) Rs 1846
• 4) Rs 1960
• Discussion in forum
Solution : Area of first room = 2(l + b)*h
After all dimensions doubled, new area = 2(2l + 2b)*2h = 4[2(l + b) * h ] = 4 times previous area, so cost of painting = 4 * 475

discussion

• ( 6 ) What will be the cost of painting a hall whose area is 256sq m, if the rate of painting per sq m is Rs.22.

• 1) Rs.1256
• 2) Rs.1350
• 3) Rs.2225
• 4) Can't be determined
• Discussion in forum
Answer : 4) Can't be determined
Solution : Hall shape and it's parameter was not given

discussion

Answer : 4) Can't be determined

• ( 7 ) A right triangle with sides 15,16 and 18cm is rotated about the side 15cm to form a cone. The volume of the cone will be

• 1) 4011.65 cubic cm
• 2) 3022.65 cubic cm
• 3) 4022.85 cubic cm
• 4) 2022.65 cubic cm
• Discussion in forum
Answer : 3) 4022.85 cubic cm
Solution : h = 15, r = 16
Volume= 1/3* π * (16)2 * 15

discussion

Answer : 3) 4022.85 cubic cm

• ( 8 ) 5m radius and 12m height solid metallic cylinder is melted and recast into small spherical balls of radius 5m. Find the no of cubes that can be made ?

• 1) 3
• 2) 2
• 3) 4
• 4) 5
• Discussion in forum
Solution : Volume of cylinder = volume of cube
(3.14 * 5 * 5 * 12) = N(4/3 * 3.14 * 5 * 5 * 5)
N = (12 * 3)/(4 * 5) = 1.8 = 2

discussion

• ( 9 ) The side of a cube is 13 cm, Find its surface area?

• 1) 1014 cm2
• 2) 1040 cm2
• 3) 1010 cm2
• 4) 1024 cm2
• Discussion in forum
Solution : Surface area = 6a2 = 6 * 13 * 13 = 1014cm2

discussion

• ( 10 ) Shalu wishes to start a 78sq m triangular flower garden. Since she has only 20m barbed wire, she fences three sides of the garden letting her house compound wall act as the fourth side fencing. The dimension of the garden is

• 1) 26m*3m
• 2) 14m*3m
• 3) 25m*5m
• 4) 12m*3m
• Discussion in forum
Solution : L = 20 - 2b
area of the garden = 78 sq m,
L * b =78
b*(20-2b) = 78
20b - 2b2 = 78
b2 -10b + 39 = 0
b = 3 b = 13
b = 3 then L = 26
b = 13 then L = 6
Dimension = 26m * 3 m

discussion