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Volume and Surface Area Online Test Details
| Quiz Name | Volume and Surface Area |
| Category | Aptitude |
| Number of Questions | 16 |
| Time | 30 Minutes |
| Exam Type | MCQ (Multiple Choice Questions) |
Volume and Surface Area Quiz Online Test – Practise Now
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1. If the ratio of the length of two rectangles is 7:8 and the breadth in the ratio of 2:3, find the ratio of the area of the rectangles?
A. 3:4
B. 5:9
C. 3:8
D. 1:2
E. None of these
Answer: E
Explanation:
Area of the rectangle = lb
The ratio of the breadth of two rectangles =2: 3 (2y, 3y)
Required ratio = 7x * 2y:8x * 3y =7:12
2. If the perimeter of a square is 32 cm, find the area of square whose side is 2 times the earlier square.
A. 64 cm²
B. 132 cm²
C. 256 cm²
D. 144 cm²
E. 196 cm²
Answer: C
Explanation:
Side = perimeter /4 = 32/4 = 8cm
Side of new square = 16
Area of new square = a2
= 16 * 16 = 256 cm²
3. Perimeter of the square is 84 cm and the radius of the sphere is two-third of the side of the square. What is the surface area of the sphere?
A. 2464 cm²
B. 2434 cm²
C. 2454 cm²
D. 2646 cm²
E. None of these
Answer: A
Explanation:
Perimeter of the square = 4 * a 84 = 4 * a
Side of the square = 84/4 = 21 cm
Radius of the sphere = 2/3 * 21 = 14 cm
Surface area of the sphere = 4 * 22/7 * r * r
= 4 * 22/7 * 14 * 14
= 2464 cm²
4. The circumference of a circle is equal to the perimeter of a square. The side of the square is 55 cm. What is double the diameter of the circle?
A. 35 cm
B. 120 cm
C. 140 cm
D. 84 cm
E. 70 cm
Answer: C
Explanation:
The circumference of a circle is equal to the perimeter of a square = 2πr
= 4a 2 * 22/7 * r
= 4 * 55
r = 35
Diameter = 2r = 70
Double the diameter of the circle = 2 * 70
= 140
5. The perimeter of the triangle is 18 cm and the side of the square is equal to the side of the triangle. What is the area of the square?
A. 25 cm²
B. 64 cm²
C. 49 cm²
D. 36 cm²
E. None of these
Answer: D
Explanation:
Perimeter of the triangle = 3 * a
= 18 a = 6 cm
Area of the square = 6 * 6
= 36 cm2
6. If the length of the rectangle is increased by 20% and the breadth of the rectangle is decreased by 15%, then find the increase or decrease of the area of the rectangle?
A. 1% decrease
B. 2% increase
C. 5% decrease
D. 4% increase
E. None of these
Answer: B
Explanation:
Let initial Area of the rectangle
= 100 100 * 120/100 * 85/100
= 102
Area = 2% increase
7. If the area of the trapezium is 126 cm² and the base of the trapezium is 16 cm and 12 cm respectively, then what is the height of the trapezium?
A. 12 cm
B. 8 cm
C. 9 cm
D. 11 cm
E. None of these
Answer: C
Explanation:
Area of the trapezium = 1/2(a + b) * h
126 = 1/2 * (16 + 12) * h
h = 9 cm
8. The ratio of the length and the breadth of a rectangle is 15:8 and the area of the rectangle is 1080 sq.cm. What is the perimeter of the rectangle?
A. 108 cm
B. 118 cm
C. 128 cm
D. 138 cm
E. None of these
Answer: D
Explanation:
Ratio of length and the breadth of a rectangle = 15:8 (15x, 8x)
Area of the rectangle = l * b= 1080 sq cm (15x) (8x)
(15x) (8x ) = 1080
x2 = 1080/120 = 9
x= √ 9 = 3
Length = 15 * 3 = 45 cm
Breadth = 8 * 3 = 24 cm
Perimeter of the rectangle = 2 (l + b)
= 2 (45 + 24)= 138 cm.
9. Ratio of the length to breadth of the rectangular floor is 2:1. If Rs.1440 is required to paint the floor at the rate of Rs.5 per square meter, then what is the difference between the length and breadth of the rectangular floor?
A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm
E. None of these
Answer: B
Explanation:
Area of the rectangle = l * b
2x * x = 1440/5=> x = 12 m
Length = 2 * 12 = 24 m
Breadth = 12 cm
Difference = 24 – 12 = 12 cm
10. The base of the triangle is equal to the diagonal of the square, whose area is 288 Sq cm. Find the area of triangle, whose height is 32 cm?
A. 384 cm²
B. 456 cm²
C. 420 cm²
D. 472 cm²
E. None of these
Answer: A
Explanation:
The diagonal of the square = (1/2) * d2 = 288 => d2 = 576
Diagonal of the square (d) = 24 cm
The area of triangle = (1/2) * b * h
= (1/2) * 24 * 32
= 384 cm²
11. The diagonal of a square is 35 √2 cm, whose area is 161 Sq cm less than the area of circle. Find the circumference of the circle?
A. 144 cm
B. 128 cm
C. 132 cm
D. 156 cm
E. None of these
Answer: C
Explanation:
The diagonal of a square = 35 √2 cm
Area of the square = (1/2) * 35 * 35 * 2 = 1225 Sq cm
Area of circle = 1225 + 161 = 1386 Sq cm
(22/7) * r2 = 1386
r2 = 1386 * (7/22) = 441
Radius of the circle (r) = 21 cm
Circumference of circle = 2 * (22/7) * 21
= 132 cm
12. Total surface area of the cylinder is 1188 cm² and the sum of the radius and height of the cylinder is 27 cm. What is the volume of the cylinder?
A. 616 cm²
B. 1232 cm^3
C. 2640 cm^3
D. 3080 cm^3
E. None of these
Answer: D
Explanation:
TSA = 2 * 22/7 * r * (h + r)
1188 = 2 * 22/7 * r * 27
Radius of the cylinder = 7 cm
Height of the cylinder = 27 – 7 = 20 cm
Volume of the cylinder = 22/7 * r * r * h
= 22/7 * 7 * 7 * 20
= 3080 cm^3
13. The ratio of the height to radius of the cone is 3: 1 and the ratio of the radius of circle to cone is 2:1. If the circumference of the circle is 88 cm, then find the volume of the cone?
A. 1078 cm^3
B. 1178cm^3
C. 1278cm^3
D. 1378cm^3
E. None of these
Answer: A
Explanation:
Circumference of the circle = 2 * 22/7 * r
88 = 2 * 22/7 * r
Radius of the circle = 14 cm
Radius of the cone = ½ * 14 = 7 cm
Height of the cone = 3 * 7 = 21 cm
Volume of the cone = 1/3 * 22/7 * r * r * h
= 1/3 * 22/7 * 7 * 7 * 21
= 1078 cm^3
14. If the ratio of the height to radius of the cylinder is 3:2 and the curved surface area of the cylinder is 1848 cm² If the radius of the cylinder is equal to the radius of the cone and the height of the cone is 9 cm, then what is the volume of the cone?
A. 1448 cm^3
B. 1648cm^3
C. 1948cm^3
D. 1848cm^3
E. None of these
Answer: E
Explanation:
Curved surface area of the cylinder= 2πrh
= 2 * 22/7 * r * h
1848 = 2 * 22/7 * 2x * 3x x
= 7 cm
Radius of the cylinder = 7 * 2 = 14 cm
Radius of the cone = 14 cm
Volume of the cone = 1/3πr2h
= 1/3 * 22/7 * r2 * h
=1/3 * 22/7 * 14 * 14 * 9
=1848 cm^3
15. The ratio of the radius and height of a right circular cone is 3: 4. If the curved surface area of the cone is 135π m2, find the total surface area of the cone.
A. 116 π m2
B. 216 π m2
C. 210 π m2
D. 110 π m2
E. 196 π m2
Answer: B
Explanation:
The ratio of the radius and height of a right circular cone = 3: 4
(3x, 4x)
Slanting height of the cone = √ (32 + 42) = 5 (5x)
The curved surface area of the cone = πrl
=> 135π = π * 3x * 5x
=> x= 3
Radius of the cone = 3 * 3 = 9 m
Height of the cone = 4 * 3 = 12 m
Slanting height of the cone = 5 * 3 = 15 m
The total surface area of the cone = πr (l + r)
=> π * 9 * (15 + 9)
= 216π m2
16. If the ratio of the radius of the circle to the cylinder is 1: 2 and the height of the cylinder is 8 cm more than the radius of the cylinder. If the circumference of the circle is 22 cm, then what is the volume of the cylinder?
A. 2110 cm^3
B. 2210cm^3
C. 2310cm^3
D. 2410cm^3
E. None of these
Answer: C
Explanation:
Circumference of the circle = 2 * 22/7 * r
2 * 22/7 * r = 22
Radius of the circle = 3.5 cm
Radius of the cylinder = 2 * 3.5 = 7 cm
Height of the cylinder = 7 + 8 = 15 cm
Volume of the cylinder = 22/7 * r * r * h
= 22/7 * 7 * 7 * 15
= 2310 cm^3
17. The radius of the cone is equal to the radius of the cylinder and the ratio of the radius and the height of the cylinder is 7:9 respectively. If the curved surface area of the cylinder and the volume of the cone is 1584 cm² and 1848 cm^3, then find the height of the cone?
A. 10 cm
B. 7 cm
C. 11 cm
D. 9 cm
E. None of these
Answer: D
Explanation:
Let the height of the cylinder=9x
The radius of the cylinder=7x 2*22/7*9x*7x
=1584
x2=4
x=2
Radius of the cone=7*2=14 cm
Height of the cone=h
Volume of the cone=1848 cm^3
1/3*22/7*14*14*h=1848
h=9 cm
18. The volume of the cuboid is 4320 cm^3 and the height of the cuboid is 8 cm more than its breadth. If the length of the rectangle and cuboid is x cm and (x – 6) cm respectively and the perimeter of the rectangle is 80 cm and the breadth of the rectangle is 20% of its perimeter, then find the height of the cuboid?
A. 24 cm
B. 20 cm
C. 28 cm
D. 30 cm
E. 25 cm
Answer: B
Explanation:
Breadth of cuboid = a
Breadth of the rectangle = 20/100 * 80 = 16 cm
Length of the rectangle = (80/2) – 16 = 24 cm
Length of cuboid = 24 – 6
= 18 cm a * (a + 8) * 18= 4320
a2 + 8a = 240
a2 + 20a – 12a – 240 = 0
a(a + 20) – 12(a + 20) = 0 a = 12
Height of the cuboid = 12 + 8 = 20 cm
19. The ratio of radius of cone to cylinder is 1: 2 and the curved surface area of the cone is 396 cm² If the slanting height of the cone is 18 cm and volume of the cylinder is 2464 cm^3, then find the total surface area of the cylinder
A. 1284 cm²
B. 1384 cm²
C. 1484 cm²
D. 1584 cm²
E. None of these
Answer: D
Explanation:
CSA of the cone = 22/7 * r * l
396 = 22/7 * r * 18
Radius of the cone = 7 cm
Radius of the cylinder = 2 * 7 = 14 cm
Volume of the cylinder = 2464 cm^3
= πr2h (i.e.) 22/7 * 14 * 14 * h = 2464
Height of the cylinder = 4 cm
TSA of cylinder = 2 * 22/7 * r * (h + r)
= 2 * 22/7 * 14 * (4 + 14)
= 1584 cm²
20. If the ratio of the length to breath of the rectangle is 2: 1 and the radius of the cylinder is equal to the breadth of the rectangle. If the height of the cylinder is three – fourth of the length of the rectangle whose perimeter is 84 cm, then what is the volume of the cylinder?
A. 4116 π cm^3
B. 4136 π cm^3
C. 4216 πcm^3
D. 4146 πcm^3
E. None of these
Answer: A
Explanation:
Perimeter of the rectangle = 2 * (l + b) = 84 cm
2 * (3x) = 84 x = 14 cm
Length of the rectangle = 2 * 14 = 28 cm
Breadth of the rectangle = 14 cm
Radius of the cylinder = 14 cm
Height of the cylinder = 3/4 * 28 = 21 cm
Volume of the cylinder = 22/7 * r * r * h
= 22/7 * 14 * 14 * 21
= 4116 π cm^3
21. If the radius of the circle is increased by 20% then the area of the circle becomes 887.04 cm² and the radius of the cone is half of the radius of circle and the height of the cone is 11 cm more than the radius of the cone, then find the volume of the cone?
A. 936 cm^3
B. 928 cm^3
C. 924 cm^3
D. 932 cm^3
E. None of these
Answer: C
Explanation:
Radius of the circle = x
After increased the radius = x
120/100 = 6x/5
22/7 * 6x/5 * 6x/5 = 887.04 x2
= 196 x = 14 cm
Radius of the cone = 14/2 = 7 cm
Height of the cone = 11 + 7 = 18 cm
Volume of the cone = 1/3 * 22/7 * 7 * 7 * 18
= 924 cm^3
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