Question

1. The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x.

2. Find the surface area and the volume of the cylinder.

Answer 1

sa=pidh+2pir^2
v=hpir^2

d=7.2
r=7.2/2=3.6

sa=pi(7.2)(x)+2pi3.6^2
sa=7.2pix+25.92pi

V=hpir^2
V=xpi3.6^2
V=xpi12.96

SA=V so
7.2pix+25.92pi=xpi12.96
divide both sides by pi
7.2x+25.92=12.96x
minus 7.2x from both sides
25.92=5.76x
divide both sides by 5.76
4.5=x

the value of x is 4.5ft

Answer 2

x = 4.5

Surface area of the cylinder = 183.1248

Volume of Cylinder = 183.1248

Explanation:

Volume of Cylinder = πr²h

And Surface Area of Cylinder = 2πr( r + h)

where, r is radius of cylinder =
`(1)/(2) *7(1)/(5)=(36)/(10)`

and h = height of cylinder = x (unknown)

1. Surface area of the cylinder = Volume of the cylinder

⇒ πr²h = 2πr( r + h)

⇒ rh = 2(r + h)

⇒
`(36)/(10) * x = 2((36)/(10) +x)\\(36)/(10)x = (2(36+10x))/(10)`

⇒ 36x = 72 + 20x

⇒ 16x = 72

⇒ x = 4.5

2. Surface Area of Cylinder = 2πr( r + h)

`=2* 3.14*(36)/(10)*((36)/(10)+4.5 )\\=183.1248`

And, Volume of Cylinder = πr²h

= 3.14 × 3.6 ×3.6 × 4.5

= 183.1248