Solve the following math problems: 1. Circumference of base of a cylindrical tank in 176 cm and height in 30 cm. Find its curved surface area. 2. Volume of a cylinder is 44 Cubi... Solve the following math problems: 1. Circumference of base of a cylindrical tank in 176 cm and height in 30 cm. Find its curved surface area. 2. Volume of a cylinder is 44 Cubic cm and radius is 2 cm. Find its whole surface area. 3. A well whose diameter is 14m and 25m deep. Find the volume of mud taken out of the well. Also find the cost of plastering the well from inside at the rate of Rs. 3 per square metre. 4. Circumference of the base of a cylinder and height is 44m. Find its curved surface. 5. Area of curved part of a cylinder is $1000 \pi$ square cm and its diameter is 20 cm find the height of the given cylinder? Read more

Steps to Solve

Here's how we can solve each of the cylinder/well problems:

Q-2: Curved Surface Area of a Cylinder

1. Identify given values: Circumference $C = 176$ cm, height $h = 30$ cm

2. Formula for curved surface area: Curved surface area $= C \times h$

3. Calculate the curved surface area: Curved surface area $= 176 \text{ cm} \times 30 \text{ cm} = 5280 \text{ cm}^2$

Q-3: Whole Surface Area of a Cylinder

1. Identify given values: Volume $V = 44 \text{ cm}^3$, radius $r = 2$ cm

2. Find the height: The formula is: $V = \pi r^2 h$ So: $44 = \pi (2)^2 h$ $h = \frac{44}{4\pi} = \frac{11}{\pi}$ cm

3. Formula for whole surface area: Whole surface area $= 2\pi r (r + h)$

4. Calculate the whole surface area: Whole surface area $= 2\pi (2) (2 + \frac{11}{\pi}) = 4\pi(2+\frac{11}{\pi}) = 8\pi + 44 \text{ cm}^2$

Q-4: Volume of Mud and Cost of Plastering a Well

1. Identify given values: Diameter $d = 14$ m, depth $h = 25$ m, rate = Rs. 3 per square meter. Radius $r = \frac{d}{2} = \frac{14}{2} = 7$ m

2. Find the volume of the mud: The formula is: $V = \pi r^2 h$ $V = \pi (7)^2 (25) = \pi (49) (25) = 1225\pi \text{ m}^3$

3. Find the curved surface area: Curved surface area $= 2\pi r h$ Curved surface area $= 2\pi (7)(25) = 350\pi \text{ m}^2$

4. Find the cost of plastering: Cost = Curved surface area $\times$ rate Cost $= 350\pi \times 3 = 1050\pi$ Rs.

Q-5: Curved Surface Area of a Cylinder

1. Identify given values: Circumference $C = 44$ m, height $h = 44$ m.

2. Formula for curved surface area: Curved surface area $= C \times h$

3. Calculate the curved surface area: Curved Surface Area $= 44 \text{ m} \times 44 \text{ m} = 1936 \text{ m}^2$

Q-6: Height of a Cylinder

1. Identify given values: Curved surface area $= 1000\pi \text{ cm}^2$, diameter $= 20$ cm, so radius $r = 10$ cm.

2. Formula for curved surface area: Curved surface area $= 2\pi r h$

3. Find the height: $1000\pi = 2\pi (10) h$ $1000\pi = 20\pi h$ $h = \frac{1000\pi}{20\pi} = 50$ cm