Volume and Surface Area Questions with Solutions
Introduction
Volume and surface area problems are fundamental concepts in geometry that play a crucial role in various fields, including mathematics, engineering, and architecture. These problems require a deep understanding of concepts of space and the ability to apply mathematical formulas to solve real-world challenges. Whether you're preparing for an exam or any other competitive assessment, mastering volume and surface area problems is essential. In this Nithra Jobs article, we will delve into a range of volume and surface area problems with solutions that you might encounter during your exams.
1. The radius of the base of cone is 4 cm and height is 9 cm. Find the volume of the cone?Answer: 48 π cm3
Explanation:
Given data,
The radius of the base of cone = 4 cm
Height = 9 cm
Formula,
Volume of the cone = ( 1 / 3 ) * π * r2 * h
= ( 1 / 3 ) * π * 4 * 4 * 9
= 48 π cm3
The volume of the cone is 48 π cm3.
2. The area of a base of a cone is 40 cm2. If the height of the cone is 12 cm, find its volume?
Answer: 160 cm3
Explanation:
Given data,
The area of the base of cone = 40 cm2
Height = 12 cm
Formula,
Volume of the cone = ( 1 / 3 ) * π * r2 * h
The area of the base of cone, π * r2 = 40 cm2
Volume of the cone = ( 1 / 3 ) * π * r2 * h
= ( 1 / 3 ) * 40 * 12
= 160 cm3
The volume of the cone is 160 cm3.
3. A room is 16 m long, 5 m broad and 3m height. Find the cost of white washing its four walls at Rs. 3 per m2?
Answer: Rs. 378
Explanation:
The total area of the four walls = 2 * height (length + broad)
= 2 * 3 ( 16 + 5 )
= 6 * 21
= 126
The cost of white washing its four walls at Rs. 3 per m2 = 126 * 3
= Rs. 378
The cost of white washing its four walls at Rs. 3 per m2 is Rs. 378.
4. Two cylinders are of the same height. Their radii are in the ratio 1 : 4. If the volume of the first cylinder is 45 cc. Find the volume of the second cylinder?
Answer: 720 cc
Explanation:
Let the radius of the first cylinder, r1 = 1x
The radius of the second cylinder, r2 = 4x
Formula for the volume of the cylinder = π * r2 * h
Given,
The volume of the first cylinder = π * x2 * h = 45cc
Then, the volume of the second cylinder = π * ( 4x )2 * h
π * ( 4x )2 * h = 16 * ( π * x2 * h )
= 16 * 45
= 720 cc
The volume of the second cylinder = 720 cc.
5. Find the length of the wire required to go 15 times round a square field containing 70756 m2?
Answer: 15960 m
Explanation:
Given,
To find the length of the wire?
The volume of square = a2
a2 = 70756 m2
a = 266 m
The perimeter of square = 4a
= 4 * 266
= 1064
The length of the wire required to go 15 times round a square field = 15 * 1064
= 15960 m
The length of the wire is 15960 m.
Problems for practice:
1. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
2. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
3. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
4. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
5. A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
Conclusion
Volume and surface area problems with answers are essential components of any competitive exam, As you prepare for your exam, remember to practice these concepts regularly to reinforce your skills. Utilize this knowledge to solve complex problems efficiently and accurately. With dedication and practice, you can excel in the volume and surface area section of your exam and position yourself for success in your pursuit of a fulfilling career. Good luck!
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