Find the length of the longest pole that can be placed in a room 12 m long, 8m broad and 9 m high.
Answer: B
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Radius of a cylinder is equal to the side of an equilateral triangle having area 16√3 cm⊃2; and height of the cylinder is equal to the perimeter of the triangle. Then find the volume of cylinder.
Answer: A
Area of equilateral triangle = 16√3 cm⊃2;
WKT, Area of equilateral triangle = √3/4 a2
√3/4 a⊃2; = 16√3
a⊃2; = 64
a = 8 cm
Side of an equilateral triangle = Radius of a cylinder
a = r
r = 8cm
Perimeter of equilateral triangle = 3a = 3(8) = 24 cm
Perimeter of equilateral triangle = Height of cylinder
So, h = 24 cm
Volume of cylinder = πr⊃2;h
= π x 8 x 8 x 24
= 1536π cm⊃3;.
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Each side of an equilateral triangle is 6 cm. Find its area.
Answer: A
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There were two solid spherical balls. Ratio between radius of first ball to that of second ball is 4 : 3. Second ball was cut into two equal halves and the difference between total surface area of first ball and total surface area of a part of second ball is 1424.5 cm⊃2;. Find value of radius of bigger ball ?
Answer: A
Ratio between radius of first ball to that of second ball is 4 : 3.
Let the radius of first ball be '4r' and radius of second ball be '3r'.
When we cut the second ball it become hemisphere.
WKT, Total surface area of sphere = 4π r⊃2;
Total surface area of hemisphere = 3π r⊃2;
As per the question,
4 x (22/7) x (4r)⊃2; - 3 x (22/7) x (3r)⊃2; = 1424.5
(22/7)*r⊃2;[64 - 27] = 1424.5
r⊃2; = [1424.5*7]/[37*22]
r⊃2; = 12.25
r = 3.5 cm
Therefore, radius of bigger ball = 4r = 4(3.5) = 14 cm.
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The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Answer: D
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The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Answer: D
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l⊃2; + b⊃2;) = (1 + 108 1/3 %)lb
=> l⊃2; + b⊃2; = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b⊃2;)/lb = 25/12
12(l2 + b⊃2;) = 25lb
Adding 24lb on both sides
12l2 + 12b⊃2; + 24lb = 49lb
12(l2 + b⊃2; + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)⊃2; = 49lb
=> 12(14)⊃2; = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
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Length of a rectangle is 12cm more than its breadth and it has a perimeter of 200cm. What will be diameter of a circle whose area matches the area of this rectangle?
Answer: B
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Which of the following has its area and perimeter numerically equal?
Answer: C
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By converting angle from degrees to radians, 105° is equal to
Answer: D
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The length and breadth of a rectangle are in the ratio of 9:5. When the sides of the rectangle are extended on each side by 5 m the ratio of length to breadth becomes 5:3. What is the area of the original rectangle?
Answer: C
Let the length and breath of rectangle be 'X' m and 'Y' m respectively.
Given, length and breadth of a rectangle are in the ratio of 9 : 5.
X/Y = 9/5
5X = 9Y
5X - 9Y = 0 ....(i)
If sides of the rectangle are extended by 5 m, ratio becomes 5 : 3.
(X + 5)/(Y + 5) = 5/3
3(X + 5) = 5(Y + 5)
3X + 15 = 5Y + 25
3X - 5Y = 10 ....(ii)
By solving equation (i) and (ii),
X = 45 m ; Y = 25 m
So, length of rectangle = 45 m
Breadth of rectangle = 25 m
WKT, Area of rectangle = l x b
Area of rectangle = 45 x 25 = 1125 sq.m.
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