Question

A rectangular sheet of dimensions 44 cm x7 cm is rotated about its longer side. Find the volume and the total surface area of the solid thus generated.​

Answer 1

Step-by-step explanation:

Given :-

A rectangular sheet of dimensions 44 cm x7 cm is rotated about its longer side.

To find :-

The volume and the Total Surface Area of the solid thus generated.

Solution :-

Given that

The dimensions of a rectangular sheet

= 44 cm × 7 cm

The longer side = 44 cm

According to the given problem

The sheet is rotated about ists longer side then

The resultant solid is a cuboid and the longer side becomes it's circumference and the shorter side becomes it's height.

Therefore, Height = 7 cm

We know that

The circumference of a cuboid =

The circumference of a circle = 2πr units

Therefore, 2πr = 44 cm

=> 2×(22/7)×r = 44

=> (44/7)×r = 44

=> r = 44×(7/44)

=> r = 7 cm

Therefore, Radius of the cuboid = 7 cm

i)

We know that

Volume of a cuboid (V) = πr²h cubic units

Volume of the cuboid = (22/7)×7²×7 cm³

=> V = (22/7)×7×7×7

=> V = 22×7×7

=> V = 1078 cm³

Volume of the resultant cuboid

= 1078 cm³

ii)

We know that

Total Surface Area of a cuboid

= 2πr(r+h) sq.units

Total Surface Area of the cuboid

=> TSA = 2×(22/7)×7(7+7) cm²

=> TSA = 2×(22/7)×7×14

=> TSA = 2×22×14

=> TSA = 616 cm²

Total Surface Area = 616 cm²

Answer :-

Volume of the resultant cuboid

= 1078 cm³

Total Surface Area of the resultant cuboid = 616 cm²

Used formulae:-

→ Circumference of a circle = 2πr units

→ Volume of a cuboid = πr²h cubic units

→ Total Surface Area of a cuboid

= 2πr(r+h) sq.units

• r = radius
• h = height
• π = 22/7

Answer 2

Answer:

The volume and the surface area of the cylinder are 6776 cm³ and 2244 cm² respectively.

Step-by-step explanation:

The length of the rectangle = 44 cm

The width of the rectangle = 7 cm

It is given that the rectangle is rotated about its longer side. Thus the formed solid will be a cylinder.

Then the height (h) of the cylinder = 44 cm

The radius (r) of the cylinder = 7 cm

The formula to find the volume of the cylinder is given as,

          V = πr²h  

The value of π = $\frac{22}{7}$  

By substituting the values,

⇒         V = $\frac{22}{7}$ × 7² × 44

              = 22 × 7 × 44

              = 6776 cm³

The formula to find the surface area is given as,

          S = 2πr(r + h)

By substituting the values,

⇒         S = (2 × $\frac{22}{7}$ × 7)(7 + 44)

              = (2 × 22)(51)

              = 44 × 51

               = 2244 cm²

Here we took the value of π as $\frac{22}{7}$, because we can do the calculations easily.

Hence the volume and the surface area of the cylinder are 6776 cm³ and 2244 cm² respectively.