Question

Determine to the nearest and tenth the surface area of a tin can with a radius of 8 centimeters and a height of 16 centimeters

Answer 1

Answer:

1206 square centimeters

Step-by-step explanation:

Hello, I can help you with that

a tin is a cylinder,a cylinder is formed by 2 circles anda 1 rectangle

let's remember

Area of the circle

$A=\pi *radius^{2}$

Area of the rectangle

$A_{r}=length *wide$

the length of the rectangle is the height of the tin  (16 cm)

and the wide is equal to the perimeter of the circle

perimeter of the circle(P)

$P=2*\pi *radius$

so, the area of the rectangle is

$A_{r}=length *wide\\\\A_{r}=heigth *2*\pi *radius$

Step one

find the total area:

the total area is equal to 2 circles + 1 rectangle

$A_{total}=(2* \pi *radius^{2} )+(height*2*\pi *radius)$

Step two

put the values into the equation

height = 16 cm

radius= 8 cm

$A_{total}=(2* \pi *radius^{2} )+(height*2*\pi *radius)\\A_{total}=(2* \pi )+(16*2*\pi *8)\\A_{total}=(128* \pi )+(256*\pi )\\A_{total}= 378 \pi\\ A_{total}=1206.37$

so, the total area is 1206.37 square centimeters

I hope it helps, have a great day.

Answer 2

Answer:

The surface area of the tin can is 1206.37cm²

Step-by-step explanation:

The tin can is cylindrical in nature and the surface area of a cylinder is expressed as;

S = 2πr(r+h)

r is the radius of the tin can

h is the height of the tin can

Given r = 8cm

h = 16cm

To get the surface area, we will substitute the given parameters into the formula to have;

S = 2π(8){8+16}

S = 16π×24

S = 1206.37cm²