Question

The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110cm. find the heights and the volume of the cylinder. Plz Urgent ​

Answer 1

Answer:

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Therefore the height of the cylinder is 39.99 cm . Put in the formula of volume of a cylinder . Therefore the height of the cylinder is 39.99 cm and volume of the cylinder is 38543.332 cm³ .

Step-by-step explanation:

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Answer 2

As per the given information in the question, we have:

• The curved surface area of cylinder is 4400 cm².
• The circumference of it's base is 110 cm.

We have been asked to find the height and volume of cylinder.

– We know, curved surface area of the cylinder is given by 2πrh and the circumference of the base of the cylinder is given by 2πr. Here, we know the value of circumference of the base and the value of π. Let us substitute this value in 'Circumference of base' formula, in order to find the radius.

$\longrightarrow\: \: \: \sf{Circumference\: of\: base=2\pi r}$

Substituting, value of circumference of base as 110 cm and value of π as 22/7,

$\longrightarrow\: \: \: \sf{110=2\times \dfrac{22}{7}\times r}$

Multiplying, 2 and 22/7,

$\longrightarrow\: \: \: \sf{110=\dfrac{44}{7}\times r}$

Transposing, 7 from RHS to LHS and performing multiplication with 110,

$\longrightarrow\: \: \: \sf{110\times 7=44\times r}$

Multiplying 110 and 7,

$\longrightarrow\: \: \: \sf{770=44\times r}$

Transposing, 44 from RHS to LHS and performing division with 770,

$\longrightarrow\: \: \: \sf{\dfrac{770}{44}=r}$

Performing division on LHS side,

$\longrightarrow\: \: \: \bold{r=17.5\: cm}$

$\: \: \: \: \leadsto$Hence, radius of the cylinder is 17.5 cm.

Now, let us calculate the height of the cylinder, in order to find the height of the cylinder, firstly we need to equate all the values in 'Curved surface area of cylinder formula' $\\ \longrightarrow\: \: \: \sf{Curved\: surface\: area\: of\: cylinder=2\pi rh}$

Substituting, curved surface area of cylinder as 4400 cm² , π as 22/7 and radius as 17.5 cm.

$\longrightarrow\: \: \: \sf{4400=2\times \dfrac{22}{7}\times 17.5\times h}$

Multiplying, 22/7 and 2,

$\longrightarrow\: \: \: \sf{4400=\dfrac{44}{7}\times 17.5\times h}$

Multiplying, 44/7 and 17.5,

$\longrightarrow\: \: \: \sf{4400=\dfrac{770}{7}\times h}$

Dividing, 770 by 7,

$\longrightarrow\: \: \: \sf{4400=110\times h}$

Transposing, 110 from RHS to LHS and performing division,

$\longrightarrow\: \: \: \sf{\dfrac{4400}{110}=h}$

Performing division,

$\longrightarrow\: \: \: \bold{h=40\: cm}$

$\: \: \: \: \leadsto$ Hence, height of cylinder is 40 cm.

— According to the given question, we have to find the volume of cylinder. Volume of cylinder is given by πr²h. So, equating all the values, we get:

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

Substituting, π as 22/7, r as 17.5 cm and h as 40 cm.$\\ \longrightarrow\: \: \: \sf{Volume\: of\: cylinder= \dfrac{22}{7}\times {17.5}^{2}\times 40}$

Equating, square of 17.5 as 306.25. $\\\longrightarrow\: \: \: \sf{Volume\: of\: cylinder= \dfrac{22}{7}\times 306.25\times 40}$

Multiplying, 306.25 and 40

$\longrightarrow\: \: \: \sf{Volume\: of\: cylinder= \dfrac{22}{7}\times 12250}$

Multiplying, 22/7 and 12250, $\\\longrightarrow\: \: \: \bold{Volume\: of\: cylinder=38500\: {cm}^{3}}$

❝ Therefore, height of the cylinder is 40 cm and it's volume is 38500 cm³. ❞