A rectangular strip 25cm*7cm is rotated about the longer side. find the total surface area of the solid thus generated.

Take a small rectangular piece of paper, such as a business card, hold a finger on the end of the longer side and rotate the card.

What do you notice ?

Nice

Aao

You do practically

To find the total surface area of the solid generated when a rectangular strip is rotated about its longer side, we need to calculate the curved surface area and the two circular base areas.

First, let's calculate the curved surface area. When a rectangle is rotated about its longer side, it forms a cylinder. The curved surface area of a cylinder can be found using the formula:

Curved Surface Area = 2 * π * r * h

Here, r is the radius of the circular base, and h is the height of the rectangle, which is also the width of the strip.

In this case, the longer side of the rectangle is 25 cm, which becomes the circumference of the circular base. Therefore, we can find the radius (r) by dividing the circumference by 2π:

25 cm = 2πr
r = 25 cm / (2π)

Now we need to find the height (h) of the rectangle, which is 7 cm, as given.

Thus, the curved surface area (CSA) is:

CSA = 2 * π * r * h
= 2 * π * (25 cm / (2π)) * 7 cm

Simplifying, we get:

CSA = 25 cm * 7 cm
= 175 cm²

Next, let's calculate the base areas. Since the shape formed by rotating a rectangle has circular bases, each base is a circle.

The area of a circle is given by the formula:

Area = π * r^2

Both bases have the same radius as calculated earlier:

Base Area = 2 * π * (r^2)
= π * (25 cm / (2π))^2
= π * (25 cm)^2 / (4π^2)
= (625 cm²) / (4π)

Now, to find the total surface area (TSA), we add the curved surface area and the two base areas:

TSA = CSA + 2 * Base Area
= 175 cm² + 2 * (625 cm²) / (4π)

Simplifying, we get:

TSA = 175 cm² + (1250 cm²) / (4π)

Therefore, the total surface area of the solid generated by rotating the rectangular strip is 175 cm² + (1250 cm²) / (4π) cm².

1408 cm²