Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
The inner diameter of circular well is 3.5 m. It is 10m deep. Its inner curved surface area in m² is:
Explanation: The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the depth (or height) of the well. From the problem: - The inner diameter of the well is 3.5 m, so the radius (r) is: r = DiameterRead more
Explanation:
The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the depth (or height) of the well.
From the problem:
– The inner diameter of the well is 3.5 m, so the radius (r) is:
r = Diameter / 2 = 3.5 / 2 = 1.75 m,
– The depth (h) of the well is 10 m.
Substitute the values of r = 1.75 m and h = 10 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 1.75 × 10.
Simplify step by step:
CSA = 2 × (22/7) × 17.5,
CSA = 2 × 22 × 2.5,
CSA = 110 m².
Thus, the inner curved surface area of the well is 110 m², which corresponds to option b) 110.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. The area of the playground in m² is :
Explanation: The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is: CSA = 2πrh, where: - r is the radius of the circular base, - h is the length (or height) of the cylinder. From the problem: -Read more
Explanation:
The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the length (or height) of the cylinder.
From the problem:
– The diameter of the roller is 84 cm, so the radius (r) is:
r = Diameter / 2 = 84 / 2 = 42 cm = 0.42 m (converted to meters),
– The length (h) of the roller is 120 cm = 1.2 m (converted to meters).
Substitute the values of r = 0.42 m and h = 1.2 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 0.42 × 1.2.
Simplify step by step:
CSA = 2 × (22/7) × 0.504,
CSA = 2 × 22 × 0.072,
CSA = 3.168 m².
This is the area covered by the roller in one complete revolution. Since the roller takes 500 revolutions to level the playground, the total area of the playground is:
Total Area = CSA × Number of Revolutions,
Total Area = 3.168 × 500,
Total Area = 1584 m².
Thus, the area of the playground is 1584 m², which corresponds to option a) 1584.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
A metal pipe is 77 cm long. Inner diameter of cross section is 4 cm and outer diameter is 4.4 cm. Its inner curved surface area is:
Explanation: The inner curved surface area (CSA) of a cylindrical pipe is given by the formula: CSA = 2πrh, where: - r is the inner radius of the circular base, - h is the height (or length) of the cylinder. From the problem: - The length (h) of the pipe is 77 cm, - The inner diameter of the cross-sRead more
Explanation:
The inner curved surface area (CSA) of a cylindrical pipe is given by the formula:
CSA = 2πrh,
where:
– r is the inner radius of the circular base,
– h is the height (or length) of the cylinder.
From the problem:
– The length (h) of the pipe is 77 cm,
– The inner diameter of the cross-section is 4 cm, so the inner radius (r) is:
r = Diameter / 2 = 4 / 2 = 2 cm.
Substitute the values of r = 2 cm and h = 77 cm into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 2 × 77.
Simplify step by step:
CSA = 2 × (22/7) × 154,
CSA = 2 × 22 × 22,
CSA = 968 cm².
Thus, the inner curved surface area of the metal pipe is 968 cm², which corresponds to option b) 968 cm².
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of its circular base is
Explanation: The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the height of the cylinder. From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula: 88 = 2πr(14). SRead more
Explanation:
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the height of the cylinder.
From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula:
88 = 2πr(14).
Simplify:
88 = 28πr.
Divide both sides by 28π to isolate r:
r = 88 / (28π).
Using π ≈ 22/7 for calculation:
r = 88 / (28 × 22/7),
r = 88 / (4 × 22),
r = 88 / 88,
r = 1 cm.
The diameter (d) of the circular base is twice the radius:
d = 2r = 2 × 1 = 2 cm.
Thus, the diameter of the circular base is 2 cm, which corresponds to option d) 2 cm.
See lessTwo cubes each of edge 12 cm are joined. The surface area of new cuboid is
Explanation: Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows: - Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges), - Breadth (b) = 12 cm (same as the edge of one cube), - HeigRead more
Explanation:
Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows:
– Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges),
– Breadth (b) = 12 cm (same as the edge of one cube),
– Height (h) = 12 cm (same as the edge of one cube).
The surface area of a cuboid is given by:
Surface Area = 2(lb + bh + lh).
Substitute the values of l = 24 cm, b = 12 cm, and h = 12 cm:
Surface Area = 2[(24 × 12) + (12 × 12) + (24 × 12)].
Calculate each term:
24 × 12 = 288,
12 × 12 = 144,
24 × 12 = 288.
Add these values:
288 + 144 + 288 = 720.
Multiply by 2:
Surface Area = 2 × 720 = 1440 cm².
Thus, the surface area of the new cuboid is 1440 cm², which corresponds to option b) 1440 cm².
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/