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

• Radius of the base of cylinder is 14 cm.
• Volume of cylinder is 3080 cm³.

Step-by-step explanation:

Given:-

• Curved surface area of cylinder is 440 cm².
• Height of cylinder is 5 cm.

To find:-

• Radius of base of cylinder.
• Volume of cylinder.

Solution:-

We know,

$\boxed{\sf \bold{Curved\: surface \: area \: of \: cylinder = 2 \pi r h}}$

Where, r is radius of cylinder and h is height of cylinder.

Put the values :

$\longrightarrow$ 2πrh = 440

$\longrightarrow$ 2 × 22/7 × r × 5 = 440

$\longrightarrow$ 44/7 × r × 5 = 440

$\longrightarrow$ 44/7 × r = 440/5

$\longrightarrow$ 44/7 × r = 88

$\longrightarrow$ 44 × r = 88 × 7

$\longrightarrow$ 44 × r = 616

$\longrightarrow$ r = 616/44

$\longrightarrow \purple{\boxed{\sf \bold{r = 14}}\star}$

Radius of base of cylinder is 14 cm.

Now,

$\boxed{\sf \bold{ Volume \: of \: cylinder = \pi r^{2} h}}$

Put the values:

$\longrightarrow$ 22/7 × (14)² × 5

$\longrightarrow$ 22/7 × 196 × 5

$\longrightarrow$ 21560/7

$\longrightarrow \red{\boxed{\sf \bold{3080}}\star}$

Therefore,

Volume of cylinder is 3080 cm³.

Answer 2

Answer:-

$\small \bf \underline{Given:}$

Curved surface area of cylinder = 440cm²

Height of cylinder = 5cm

$\small \bf \underline{To \: find:}$

We need to find

• Radius of base of cylinder
• Volume of cylinder

$\small \bf \underline{Solution:}$

» Curved surface area of cylinder = $\small\bf2πrh$

where,

r = radius of base of cylinder

h = height of cylinder

and curved surface area of cylinder = 440cm²

urved surface area of cylinder = 440cm²Height of cylinder = 5cm

So now let's substitute the given values in the formula

$\bf \: 2\pi rh = 440$

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

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

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

$\bf= > r \times 5 = 10 \times 7$

$\bf = > r = \frac{10 \times 7}{5}$

$\bf = > r = 2 \times 7$

$\bf = > r = 14$

So radius of base of cylinder = 14cm

» Volume of cylinder = $\small \bf\pi {r}^{2} h$

where,

r = radius of base of cylinder

h = height of cylinder

and radius of base of cylinder = 14cm

Height of cylinder = 5cm

Now let us substitute the values in the given formula

Volume of cylinder = $\small \bf\pi {r}^{2} h$

$\bf = \frac{22}{7} \times 14 \times 14 \times 5$

$\bf = 22 \times 2 \times 14 \times 5$

$\bf = 44 \times 70$

$\bf = 3, 080$

Therefore, volume of cylinder = 3,080cm³

Answer:

• Radius of base of cylinder = 14cm
• Volume of the cylinder = 3,080cm³

@BengaliBeauty

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