Sky Heaven is a 16 stored building with 12000 sq. feet on each floor. Zintac International rents 7 floors and Zobia International rents 4 floors. What is the number of sq. feet of unrented floor space?
There is a rectangular Garden whose length and width is 60m X 20m.There is a walkway of uniform width around garden. Area of walkway is 516m^2. Find width of walkway?
Lets assume width of rectangle = x m.
So new length will be (60+2x) and width (20+2x)
Area of walkway = 516m^2
=> (60+2x)*(20+2x)-(60*20)=516.
=> (60+2x)*(20+2x)=1716.
=> (30+x)*(10+x)=429
=> x=3m
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A spherical ball of radius 'r' placed on the ground subtends an angle of 600 at point A of the ground. What is the distance between the center of the ball and the point A?
In an equilateral triangle all three sides are of the same length and let this be 'a' units.
From the diagram it is clear that OA is the angle bisector of angle LAM.
Therefore, angle OAL = 30 In the right triangle OAL, sin 30 = OL/OA
We know that OL is the radius of the sphere = r
So,1/2 = r/OA
=> OA = 2r
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NA
SHSTTON
3
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10
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13
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Find the number of the bricks, each measuring 25 cm by 12.5 cm by 7.5 cm, required to build a wall 6 m long, 5 m high and 50cm thick, while the mortar occupies 5% of the volume of the wall.
Volume of the Wall = (600 * 500 * 50) cu. Cm.
Volume of the bricks = 95% of the volume of the wall.
= (95/100 * 600 * 500 * 50) cu. Cm.
Volume of 1 brick = (25 * 25/2 * 75/2) cu. Cm.
So, Number of bricks = (95/100 * (600 * 500 * 50 * 2 * 10)/(25 * 25 * 75))= 6080
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NA
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5
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How many squares can be formed using the checkered 1 * 1 squares in a normal chessboard?
By the relation 1^2 + 2^2 + 3^2 + 4^2 + ... + 8^2 = 204
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NA
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Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:
The length of the rope in which the horses tied should be equal to half of the side of the
square plot so that they just cannot reach one another.
Therefore, the length of the rope is 35m (70/2).
The area covered by each horse should be equal to the area of sector with radius of 70/2 = 35m(length of the rope).
Total area covered by the four horses = 4* area of sector of radius 35 metres = Area of circle of radius 35m.
Area left ungrazed by the horses = Area of square field - Area covered by four horses.
= 70^2 - (22/7)*35*35 = (4900 - 3850) = 1050 sq.m.
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NA
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2
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12
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The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?
Let ‘a’ meters be the length of a side of the square field.
So, its area = a^2 square meters. --- (1)
Length of the diagonal ‘d’ of a square whose side is ‘a’ meters = _/2*a -------- (2)
From the eq. (1) and (2)
The square of the diagonal d^2 = 2a^2
=> d = _/(2 * area) = _/(2*24200) = _/48400 = 220 meters.
The time taken to cross a length of 220 meters while traveling at 6.6 kmph = (220 meters.)/(6.6 kmph) = (220 * 60)/(6.6 * 1000) = 2 minutes.
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3
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8
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How big will an angle of one and a half degree look through a glass that magnifies things three times?
The magnifying glass cannot increase the magnitude of an angle.
Workspace
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7
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Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without travelling on the same road more than once?
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
As per the question:
(Perimeter of rectangle)/Breadth of rectangle) = 5/1
=> 2(l + b)/b = 5/1
=> 2l + 2b = 5b => 3b = 2l =>
b = (2/3)l ----------(1)
Area of rectangle = 216 cm^2
So, l x b = 216
put the value of b from eq. (1).
=> l * (2/3)l = 216 .
l*l = 324 or l^2 = 324
So, l = 18 cm.
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