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1) If the ratio of the radius of the cone to cylinder is 1: 2 and the slanting height of the cone is 25 cm. The surface area of the cone is equal to the total surface area of the sphere whose radius is 2√14 cm. If the height of the cylinder is equal to the height of the cone, then what is the curved surface area of the cylinder?
A.2612 cm2
B.2412 cm2
C.2012 cm2
D.2112 cm2
E.None of these
2) If the circumference of the circle is 44 cm and the radius of the cone is equal to the radius of the circle. The Curved surface area of the cone is 550 cm2Â and the ratio of the height of the cone to height of the cylinder is 4:3. If the ratio of the radius of the cylinder to cone is 1:2, then what is the volume of the cylinder?
A.663 cm3
B.673 cm3
C.683 cm3
D.693 cm3
E.None of these
3) If the radius of circle is 7 cm and ratio of the diameter of the circle to length of the rectangle is 1: 1, then the ratio of breadth of the rectangle to the side of the square 5: 8. If the sum of the area of circle and rectangle is 294 cm2, then what is the difference between the perimeter of the rectangle and the perimeter of the square?
A.24 cm
B.14 cm
C.17 cm
D.16 cm
E.None of these
4) If the ratio of the radius to slanting height of the cone is 3:5 and volume of the cylinder is equal to the volume of the cone. If the radius of the cylinder is 4 cm and the height of the cylinder is equal to the side of the square whose perimeter is 192 cm, then what is the curved surface area of the cone?
A.90Î cm2
B.180Î cm2
C.240Î cm2
D.Cannot be determined
E.None of these
5) If the circumference of the circle is equal to the perimeter of the square and Length of the rectangle is 8 cm more than the side of the square. If the radius of the circle is equal to the side of the equilateral triangle whose perimeter is 42 cm and the breadth of the rectangle is 6 cm more than the side of the equilateral triangle, then what is the perimeter of the rectangle?
A.80 cm
B.90 cm
C.100 cm
D.120 cm
E.None of these
6) If the total cost of the leveling in the rectangle field is Rs.10800 at the rate of Rs.9 per square meter and the side of the square is 80% of the breadth of the rectangle. If the ratio of the length and breadth of the rectangle is 4:3, then what is the difference between the perimeter of the rectangle field and square?
A.22 m
B.33 m
C.44 m
D.55 m
E.None of these
7) Perimeter of a rectangle is x meter and circumference of a circle is 52 meter more than the perimeter of the rectangle. Ratio of radius of circle and length of the rectangle is 3: 4 and ratio of length and breadth of rectangle is 7: 3. Find the area of the rectangle?
A.418 Sq m
B.352 Sq m
C.336 Sq m
D.384 Sq m
E.None of these
8) If the volume of the cone is 1232 cm3Â and the area of the rectangle is 360 cm2Â and the perimeter of the square is 60 cm. If the side of the square is equal to the breadth of the rectangle and the length of the rectangle is equal to the height of the cone, then what is the slanting height of the cone?
A.20 cm
B.22 cm
C.24 cm
D.18 cm
E.None of these
9) The radius and height of a cylinder are 15 cm and 20 cm respectively. If the radius is increased by ___ % and the height is increased by ___ %, the volume of the cylinder would increase by ___ %. Which of the following values can we fill in the same order?
(i)Â 25, 20, 87.5
(ii)Â 30, 10, 85
(iii)Â 10, 40, 70
(iv)Â 20, 25, 80
A.Only (iv)
B.Only (iii)
C.(i),(ii) and (iv)
D.Only (i) and (iv)
E.None follow
10) Area of the circle is 154 cm2Â and the radius of the cone is equal to the radius of the circle. Height of the cone is double of the height of the cylinder whose volume is 7392 cm3Â and the curved surface area of the cone is 550 cm2.
From the statement given in the above question which of the following can be determined.
a)Â Slanting height of the cone
b)Â Radius of the cylinder
c)Â Total surface area of the cylinder
d)Â If the radius of the cylinder is equal to the breadth of the rectangle whose perimeter is 68 cm, then find the area of the rectangle?
A.Only A
B.Only A and B
C.Only A, B and C
D.All A, B, C and D
E.None of these
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Answers :
1) Answer: D
Total Surface area of the sphere = 4 * 22/7 * r * r
= 4 * 22/7 * 2√14 * 2√14
= 704 cm2
Total Surface area of the cone = 22/7 * r * (l + r)
704 = 22/7 * r * (25 + r)
r = 7 cm
Radius of the cone = 7 cm
Height of the cone = √252 – 72 = 24 cm
Radius of the cylinder = 2/1 * 7 = 14 cm
Curved surface area of the cylinder = 2 * 22/7 * r * h
= 2 * 22/7 * 14 * 24 = 2112 cm2
2) Answer: D
Circumference of the circle = 2 * 22/7 * r
44 = 2 * 22/7 * r
Radius of the circle = 7 cm
Radius of the cone = 7 cm
CSA of the cone = 22/7 * r * l
550 = 22/7 * 7 * l
Slanting height of the cone = 25 cm
Height of the cone = √252 – 72 = 24 cm
Radius of the cylinder = ½ * 7 = 3.5 cm
Height of the cylinder = 3/4 * 24 = 18 cm
Volume of the cylinder = 22/7 * r * r * h
= 22/7 * 3.5 * 3.5 * 18 = 693 cm3
3) Answer: D
Area of the circle=22/7 * 7 * 7 = 154 cm2
Area of the rectangle = 294 – 154 = 140 cm2
Length * breadth = 140
Length of the rectangle = 14 cm
Breadth of the rectangle = 140/14 = 10 cm
Side of the square = 8/5 * 10 = 16 cm
Perimeter of the square = 4 * 16 = 64 cm
Perimeter of the rectangle = 2 * (l + b) = 2 * (14 + 10) = 48
Difference = 64 – 48 = 16 cm
4) Answer: C
Height of the cone = √(5x2 – 3x2) = 4x
Volume of the cone = 1/3 * 22/7 * r2Â * h
Volume of the cylinder = 22/7 * r2Â * h
Side of the square = 192/4 = 48
Height of the cylinder = 48
1/3 * 22/7 * 3x * 3x * 4x = 22/7 * 4 * 4 * 48
x = 4 cm
Radius of the cone = 3 * 4 = 12 cm
Slating height of the cone = 5 * 4 = 20 cm
CSA of the cone = 22/7 * r * l
= 22/7 * 12 * 20 = 240Î cm2
5) Answer: C
Side of the equilateral triangle = 42/3 = 14 cm
Radius of the circle = 14 cm
Breadth of the rectangle = 14 + 6 = 20 cm
Circumference of the circle = 2 * 22/7 * 14 = 88 cm
Perimeter of the square = 4 * a = 88 cm
Side of the square a = 22 cm
Length of the rectangle = 22 + 8 = 30 cm
Perimeter of the rectangle = 2 * (l + b)
= 2 * (30 + 20) = 100 cm
6) Answer: C
Area of the rectangle = 10800/9 = 1200
4x * 3x = 1200
x = 10 m
Length of the rectangle = 40 m
Breadth of the rectangle= 30 m
Side of the square = 80/100 * 30 = 24 m
Perimeter of the square = 24 * 4 = 96 m
Perimeter of the rectangle = 2 * (40 + 30) = 140 m
Difference = 140 – 96 = 44 m
7) Answer: C
Perimeter of rectangle = 2 * (l + b) = x
2l + 2b = x and 2Ï€r = x + 52
r/l = 3/4 and l/b = 7/3
r : l : b = 21 : 28 : 12 (21y, 28y, 12y)
2Ï€r = x + 52
2Ï€r = 2l + 2b + 52
Ï€r = l + b + 26
(22/7) * 21y = 28y + 12y + 26
66y = 40y + 26
26y = 26
y = 1
Length of the rectangle = 28y = 28 m
Breadth of the rectangle = 12y = 12 m
The area of the rectangle = l * b = 28 * 12 = 336 Sq m
8) Answer: E
Side of the square = 60/4 = 15 cm
Breadth of the rectangle = 15 cm
Length of the rectangle = 360/15 = 24 cm
Height of the cone = 24 cm
1232 = 1/3 * 22/7 * r * r * 24
Radius of the cone = 7 cm
Slanting height of the cone = √ (242 + 72)
= 25 cm
9) Answer: D
Suppose the radius of the cylinder is R and height is H.
Volume = πR2H
(i)
New volume = π(1.25 R)2(1.2 H) = 1.875 πR2H
Increase in volume = 87.5%
(ii)
New volume = π(1.3 R)2(1.1 H) = 1.859 πR2H
Increase in volume = 85.9%
(iii)
New volume = π(1.1 R)2(1.4 H) = 1.694 πR2H
Increase in volume = 69.4%
(iv)
New volume = π(1.2 R)2(1.25 H) = 1.8 πR2H
Increase in volume = 80%
Only (i) and (iv) satisfy the condition.
10) Answer: D
Area of the circle = 154 cm
22/7 * r * r = 154
Radius of the circle = 7 cm
550 = 22/7 * l * 7
Slanting height of the cone = 25 cm
Height of the cone = √252 – 72 = 24 cm
Height of the cylinder = 24/2 = 12 cm
7392 = 22/7 * R * R * 12
Radius of the cylinder = 14 cm
Total surface area of the cylinder = 2 * 22/7 * 14 * (12 + 14)
= 2288 cm2
2 * (14 + l) = 68
l = 20
Area of the rectangle = 20 * 14 = 280 cm2
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