Question

Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.

Answer 1

Option D

Explanation:

Let's calculate the volume first

Volume of a cylinder = πr²h
where

r = radius

h = height

Plugging in given values,
V = π x 6² x 13 = 26 x 13 = 468 in³

The only option that has this value as volume is Option D)

No need to calculate surface area

Correct answer is Option D

Answer 2

Given:-

• 
  `\rm \: radius= \bold 6 in`

`\:`

• 
  `\rm \: height = \bold {13 }in`

`\:`

To find:-

• 
  `\rm \: surface \: area = ?`

`\:`

• 
  `\rm \: volume = \: ?`

`\:`

By using formula:-

• 
  `\small \gray{\star}\boxed{ \rm \purple{ Volume \: of \: cylinder = πr²h}}`

`\:`

• 
  `\small \gray{ \star} \boxed{ \rm \color{hotpink}surface \: Area \: of \: cylinder = 2πrh + 2πr² \: }`

Solution:-

[ For surface area of cylinder ] :

• 
  `\: \rm \: surface \: area \: of \: cylinder = 2πrh + 2πr²`

`\:`

• 
  `\rm \: = 2×π × 6 × 13 + 2×π×( 6 )²`

`\:`

• 
  `\rm \: = 2π × 78 + 2π × 36`

`\:`

• 
  `\rm \: = 156π + 72π`

`\:`

• 
  `\large \boxed{\rm \green{ = 228π }}`

`\:`

value of π is 22/7.

so , if we calculate 228×22/7 then the value of surface area of cylinder is approx 716.5.

`\:`

[ For volume of cylinder ] :

• 
  `\rm \: volume \: of \: cylinder = πr²h`

`\:`

• 
  `\rm \: v = π( 6 )² × 13`

`\:`

• 
  `\rm \: v = π × 36 × 13`

`\:`

• 
  `\rm \: v = π × 468`

`\:`

• 
  `\large \boxed{\rm \color{green}v = 468π}`

`\:`

468×22/7 then the value of volume of cylinder is approx 1470.8.

hope it helps! :)