Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
Volume of a sphere: 4/3 Ï€rÂ³
Volume of a cube: xÂ³
Find the ratio meaning (4/3 Ï€rÂ³)/xÂ³
= (4Ï€/3)(rÂ³/xÂ³)
= (4Ï€/3)(r/x)Â³
= (4Ï€/3)(3 / 2Ï€)^1.5
= (2Â²Ï€/3)[3^1.5 / (2^1.5)(Ï€^1.5)]
= âˆš2âˆš3 / âˆšÏ€
= âˆš(6/Ï€)
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The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
l = 10m
h = 8m
so r = âˆš(l^2 - h^2) = âˆš(10^2 - 8^2) = 6m
So Curved surface area = (Ï€ * r * l) = ( Ï€ * 6 * 10) m2 = 60Ï€ m2.
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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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Choose the correct option.
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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Choose the correct option.
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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Choose the correct option.
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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A circular tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of conical portion is 53m, calculate the length of the canvas 5 m wide to make the required tent?
Surface area of Tent= surface area of the cylinder + surface area of the cone
=(2*pi*r*h)+ (pi*r*l)
=2*(22/7)*(105/2)*3+(22/7)*(105/2)*53
=9735 sq.m
l*b=9735
b=5m,
l=9735/5 => l=1947m
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