A builder has to pour a concrete slab 12 centimeters thick to cover an area 10 meters long and 2 meters wide. How many cubic meters of concrete will the builder need?
The distance covered by the wheel in 560 revolutions = 1100 m .
Hence, the distance covered per revolution = 1100/560 = 55/28 metres.
The distance covered in one revolution = circumference of the wheel.
Circumference = (2 * pi * r)
=> 55/28 = 2 * 22/7 * r
=> r = 31.25 cm.
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If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
Let the original length of each edge = a
Then, Original surface area = 6a^2
New surface area = 6 * (3a/2)^2 = 27a^2/2
Increase percent in surface area = (15/2a^2 * 1/(6a^2) * 100)% = 125%
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If the radius of the sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area.
Let the original radius = R. Then, new radius = 150/100 R = 3R/2
Original Volume = 4/3?R^3, New volume = 4/3?(3 R/2)^3 = 9?R^3/2
Original surface area = 4?R^2 , New surface area = 4?(3R/2)^2 = 9?R^2
Increase % in surface area = (5?R^2/4?R^2 * 100)% = 125%
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A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?
Let x be the amount of increase.
The volume will increase by the same amount if the radius increased or the height is increased.
So, the effect on increasing height is equal to the effect on increasing the radius.
=> (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3
Solving the quadratic equation
we get the x = 0 or 16/3.
So, the possible increase would be by 16/3 inches.
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Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
volume=l*b*h=6*5*2=60cm^3
now volume is reduced by 19%.therefore 81/100 *60=48.6
now,thickness remains same and let length and breadth be reduced by x%
so,new volume: 2*x/100 *6*x/100 *5=48.6
=>x=90 thus length and width is reduced by 90%
new width =90% of 5 =4.5
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A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?
The volume of the cylinder is Pi x r^2 x h = Pi x 3^2 x 6 = 54Pi
Volume of a cylinder is 4/3 x Pi x r^3
Now 54Pi = 12 x 4/3 x Pi x r^3
54 = 16 x r^3
r^3 = 54/16 = 27/8
r = 3/2
Therefore diameter is 3 cms
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Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?
Take here radius as 100.
So, surface area = 4*22/7*100*100. (Surface area of sphere = 4*pi*r^2)
As per condition:
After increase radius by 50% the new radius = 100+50% of 100=150,
So, new surface area = 4*22/7*150*150
Increase in surface area = ((4*22/7)*150*150 -(4*22/7)*100*100)/(4*22/7-100*100)=125%
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