Question

a cylinder has diameter 20 CM the area of the CSA is 1000 cm square find the height and volume of the cylinder ​

Answer 1

Answer:

The height of the cylinder is 15.9 cm.

The volume of the cylinder is 4992.6 cm³.

Step-by-step explanation:

Given : A cylinder has a diameter of 20 cm. The area of curved surface is 1000 cm².

To find :

(i) the height of the cylinder correct to one decimal place.

(ii) the volume of the cylinder correct to one decimal place.

Solution :

The diameter of a cylinder is 20 cm.

The radius of the cylinder is 10 cm.

The curved surface area of cylinder is

CSA=2\pi r hCSA=2πrh

1000=2\times 3.14\times 10\times h1000=2×3.14×10×h

h=\frac{1000}{2\times 3.14\times 10}h=

2×3.14×10

1000

h=15.9\ cmh=15.9 cm

The volume of the cylinder is

V=\pi r^2 hV=πr

2

h

V=3.14\times 10^2\times 15.9V=3.14×10

2

×15.9

V=4992.6\ cm^3V=4992.6 cm

3

#Learn more

A cylinder whose height is equal to its diameter has the same volume as a sphere of radius 4cm calculate the radius of the base of cylinder correct to one decimal place

https://brainly.in/question/2768145

Answer 2

$Given \begin{cases}The \:diameter\: of \:a \:cylinder=20cm \\ C.S.A \:of\:the\:Cylinder={1000cm }^{2}\end {cases}$

To find:-

Height and volume of the Cylinder

Solution:-

Diameter=20cm

Radius(r)=20/2=10cm

• as we know that in a Cylinder

${\boxed{C.S.A=2 {\pi }rh}}$

• Substitute the values

$2×{\dfrac {22}{7}}×10×h=1000$

${:}\longrightarrow$${\dfrac {44}{7}}×10×h=1000$

${:}\longrightarrow$${\dfrac {440}{7}}×h=1000$

${:}\longrightarrow$$h={\cancel{1000}}×{\dfrac {7}{{\cancel{440}}}}$

$\therefore$ ${\underline{\boxed{\bf {height=15.9cm}}}}$

• Now as we know that

${\boxed {volume={\pi }r {}^{2 }h }}$

• Substitute the values

$Volume={\dfrac {22}{7}}×10 {}^{2}×15.9$

${:}\longrightarrow$$Volume={\dfrac {22}{7}}×{\cancel{100}}×{\cfrac {159}{{\cancel{10}}}}$

${:}\longrightarrow$$Volume={\dfrac{22}{7}}×1590$

$\therefore$${\underline{\boxed{\bf {volume=2448.6cm{}^{3}}}}}$

Learn more:-

${\boxed{T.S.A\:of\:Cylinder=2 {\pi}r (h+r)}}$

usual value of ${\pi }={\boxed{{\dfrac {22}{7}}}}{\qquad}{\boxed {3.14}}$