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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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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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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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 â€˜aâ€™ meters be the length of a side of the square field.
So, its area = a^2 square meters. --- (1)
Length of the diagonal â€˜dâ€™ of a square whose side is â€˜aâ€™ 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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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.
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Two goats are tied with a rope of length 40m outside of a rectangular shed of dimensions 50m X 30m. The goats are tied to different corners which lie on the opposite ends of a diagonal of the shed. What is the area in which the two goats can eat grass, if they choose not to eat in the common approachable area?
Given rope of length = 40m (radius)
Area of semi circle =(pi*r^2)/2 = (1600 * pi)/2 = 800*pi ---(1)
Area of quarter circle = (1/2 * 800 * pi) = 400*pi ----- (2)
Area of sector is = r*r*(pi/2)/2 = 25*pi ----- (3)
By adding above eq. (1) (2) & (3)
Total area = 1225*pi
As per quesiton there are 2 goats
so area = 1225*pi*2 = 2450pi
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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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Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs1.50 a meter?
Formula: Area = (2 * pi * r)
Area of the field= 2 * 22/7 * 14 = 88 meter^2
So, the fencing cost = Rs 88 * 1.50 = Rs 132.
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Ms. Ganesh Mahal, Coimbatore wanted to present each of its customers with a momento rectangle in size. The momentos were of size 25 x 20 cm. The company requested the carpenter to make it in such a way that both 25 cm sides should have 24 nails each and the shorter sides should have 10 nails each. How many decorative nails the carpenter would have used in each momento?
To begin with there should be one nail in each of the corners.
There should be 22 nails on each of the two longer sides so that the count comes to 24 nails on each of those sides.
There should be 8 nails on each of the shorter sides so that the count becomes 10 nails on each of the shorter sides.
Total nails = 4 corner nails + 2 x 22 nails (longer sides) + 2 x 8 (shorter sides) = 4 + 44 + 16 = 64 nails.
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