Question

The given figure of a solid made up of cylinder and a cone. If the diameter of the cylinder is 12 cm , height 80 cm ,the slant height of the cone is 10 cm , find the total surface area of the solid object.​

Answer 1

the total surface area of the solid object is
`\bold{\green{1056\pi\: Or\:3317.52\:cm^2}}`

Answer:

Solution given:

diameter [d]=12 cm

radius [r]=
`(12)/(2)=6` cm

height of cylinder[H]=80cm

slant height [L]=10cm

Now,

Surface Area of cylinder=
`2\pi rH`

=
`2\pi *6*80=960\pi cm^2`

Surface Area of Cone:
`\pi rL`

=
`\pi *6*10=60\pi cm^2`

Surface area Base of solid=
`\pi r^2=\pi *6^2=36\pi cm^2`

The total surface area of the object:

=Surface Area of cylinder + Surface Area of Cone+ Surface area Base of solid

=
`960\pi +60\pi +36\pi`

=
`1056\pi\: Or\:3317.52\:cm^2`

Explanation:

Answer 2

`\huge\boxed{\sf 3317.5\ cm\²}`

Explanation:

Since the diameter is 12 cm, the radius will be:

r = d/2 = 12/2 = 6 cm

Now,

Surface Area of cylinder:

`= 2\pi rh+2\pi r^2\\\\Where \ r = 6 \ cm, \ h = 80 \ cm\\\\= 2(3.14)(6)(80)+2(3.14)(6)^2\\\\= 3015.9+2(3.14)(36)\\\\= 3242.12 \ cm^2`

Surface Area of Cone:

`= \pi r^2+\pi rl\\\\Where \ r = 6 \ cm, \ l = 10 \ cm\\\\= (3.14)(6)^2+(3.14)(6)(10)\\\\= (3.14)(36)+188.5\\\\= 113.1+188.5\\\\= 301.6 \ cm^2`

Surface area of the object:

= SA of cone + SA of cylinder - 2πr² (Since the base area isn't included)

= 301.6 + 3242.1 - 2(3.14)(6)²

= 3543.7 - 2(3.14)(36)

= 3543.7 - 226.2

= 3317.5 cm²

`\rule[225]{225}{2}`

Hope this helped!

~AH1807