Question

ratio of total surface area to the curved surface area of a right circular cylinder 3:2 find the volume if its total surface area is 14784 cm2

Answer 1

Answer:

137984

Step-by-step explanation:

According to question TSA/CSA=3/2

so , formula for CSA = 2πrh

formula for TSA = 2πr(h+r)

∴ 2πr(h+r)/2πr.h = 3/2

here 2πr cancel each other ,

so, we have (h+r)/h = 3/2

∴ 2(h+r) = 3h

∴2h+2r = 3h

so , 2r = 3h - 2h ⇒ 2r = h...................... (i)

now , you are given TSA of cylinder = 14784 cm∧2

∴ 14784 = 2πr(h+r)

so , 14784 = 2πr (3r)     (h = 2r)

14784 = 6πr∧2

14784/6 = πr∧2

2464= 22/7 * r∧2

so 2464*7/22 = r∧2

112*7 = r∧2

784 = r∧2

∴√784 = r

∴ r = 28

so h = 2r

∴ h = 2 (28)  ⇒ 56

now vol. of cylinder = πr∧2h

= π * 28*28*56

= 22/7 *28*28*56

= 22*28*28*8

= 22*784*8

= 176*784

= 137984

vol of cyl. = 137984

Answer 2

The volume of the cylinder is 137984 cm³.

Step-by-step explanation:

Given : Ratio of total surface area to the curved surface area of a right circular cylinder 3:2. Its total surface area is 14784 cm².

To find : The volume of the cylinder ?

Solution :

The total surface area of the cylinder is $TSA=2\pi r h+2\pi r^2$

The curved surface area of the cylinder is $CSA=2\pi r h$

Its total surface area is 14784 cm².

The ratio of total surface area to the curved surface area of a right circular cylinder 3:2.

i.e. $\frac{TSA}{CSA}=\frac{3}{2}$

$\frac{14784}{CSA}=\frac{3}{2}$

$CSA=9856$

or $2\pi r h=9856$

Now, take total surface area

$14784=9856+2\pi r^2$

$2\times \frac{22}{7}\times r^2=4928$

$r^2=\frac{4928\times 7}{2\times 22}$

$r^2=784$

$r=\sqrt{784}$

$r=28$

Substitute r in CSA,

$2\times \frac{22}{7}\times28\times h=9856$

$h=\frac{9856\times 7}{2\times 22\times 28}$

$h=56$

The volume of the cylinder is $V=\pi r^2 h$

$V=\frac{22}{7}\times(28)^2\times 56$

$V=137984\ cm^3$

Therefore, the volume of the cylinder is 137984 cm³.

#Learn more

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1:3. Find the volume of the cylinder if its total surface area is 1848cm^2

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