Question

the covered surface area of a cylinder of height 5cm is 440 square. find radius of the base and volume of cylinder​

Answer 1

The radius of cylinder is 14cm.

Question :

The curved surface area of a cylinder of height 5cm is 440 square. Find the radius of the base and volume of cylinder.

Given :

Curved Surface Area = CSA = 440 sq.units

Height of the cylinder = h = 5cm

To Find :

Radius of the cylinder = r = ?

Volume = ?

Formula Applied :

$\text{Curved Surface Area}=$$2$π$r$

$\text{Volume of Cylinder}=$π$r^{2}$

Solution :

We know that CSA of the cylinder = $2\pi rh$

And it's given that CSA = 440 sq.units and h = 5cm. So substitute values in formula,

$\implies$CSA = $2$$\pi rh$ = 440

$\implies 440 = 2\times\frac{22}{7} \times r \times 5$

$\implies 440=\frac{44}{7} \times r \times 5$

$\implies 440 \times \frac{7}{44} = r \times 5$

$\implies10\times\frac{7}{1} = 5\times r$

$\implies \frac{10\times7}{5} = r$

$\implies \textbf{r=5}$

Radius of cylinder is 5cm

As by given volume of cylinder = $\pi r^{2} h$

and r = 14, h = 5. hence substitute the values in formula

$\implies \text{Volume} = \pi r^{2}h$

$\implies \frac{22}{7} \times 14 \times 14 \times 5$

$\implies 22\times2\times14\times5$

$\implies 44\times 70$

$\implies \text{Volume}= 3080m^{3}$

Volume of cylinder is 3080cubic.units

____________________________________

$\large\textbf{Surface Area}$ :

Surface area is the measurement of all exposed area of a solid object.

$\textbf{Curved Surface Area}$ :

Curved surface area (CSA) of a right circular cylinder = Area of the corresponding rectangle

$\implies l×b$

$\implies2\pi r×h$

(since l is circumference of the base, base is the height )

$\textbf{Total Surface Area}$ :

Total surface area refers to the sum of areas of the curved surface area and the two circular regions at the top and bottom.

Total Surface Area of the right circular cylinder = C.S.A + Area of top circular region + Area of bottom circular region.

Answer 2

The radius of cylinder is 14cm.

Question :

The curved surface area of a cylinder of height 5cm is 440 square. Find the radius of the base and volume of cylinder.

Given :

Curved Surface Area = CSA = 440 sq.units

Height of the cylinder = h = 5cm

To Find :

Radius of the cylinder = r = ?

Volume = ?

Formula Applied :

Curved Surface Area= 22 πrr

Volume of Cylinder= $πr^{2}$

Solution :

We know that CSA of the cylinder = 2πrh

And it's given that CSA = 440 sq.units and h = 5cm. So substitute values in formula,

⟹ CSA = 2 πrh = 440

⟹440=2×22/7×r×5

$\implies 440=\frac{44}{7} \times r \times5$

$\implies10\times\frac{7}{1} = 5\times r$

$\implies \frac{10\times7}{5}$

$\implies \textbf{r=5}$

Radius of cylinder is 5cm

As by given volume of cylinder = πr2h

and r = 14, h = 5. hence substitute the values in formula

$\implies \text{Volume} = \pi r^{2}h$

$\implies \frac{22}{7} \times 14 \times 14 \times 5$

$\implies 22\times2\times14\times5$

$\implies 44\times 70$

$\implies \text{Volume}= 3080m^{3}$

Volume of cylinder is 3080cubic.units

____________________________________

Surface Area :

Surface area is the measurement of all exposed area of a solid object.

Curved Surface Area :

Curved surface area (CSA) of a right circular cylinder = Area of the corresponding rectangle

(since l is circumference of the base, base is the height )

Total Surface Area :

Total surface area refers to the sum of areas of the curved surface area and the two circular regions at the top and bottom.

Total Surface Area of the right circular cylinder = C.S.A + Area of top circular region + Area of bottom circular region.