[tex]\huge{\pink{\mid{\fbox{ANSWER -:}}\mid}} [/tex]

The diameter and height of the cylinder are 6 cm and 12 cm.

Volume of the rocket = volume of cylinder + volume of cone

[tex] \fbox{Volume of cylinder = πr²h}[/tex]

Given, diameter = 6 cm

Radius = 6/2 = 3 cm

h = 12 cm

Volume = (3.14)(3)²(12)

= (3.14)(9)(12)

= 339.12 cm³

[tex] \fbox{Volume of cone = (1/3)πr²h}[/tex]

Given, l = 5 cm

r = 3 cm

We know, l² = r² + h²

(5)² = (3)² + h²

25 = 9 + h²

h² = 25 - 9

h² = 16

Taking square root,

h = 4 cm

So, volume of cone = (3.14)(1/3)(3)²(4)

= (3.14)(3)(4)

= 12(3.14)

= 37.68 cm³

Volume of rocket = 339.12 + 37.68

= 376.8 cm³

Therefore, the volume of the rocket is 376.8 cm³

Total surface area of rocket = curved surface area of cylinder + curved surface area of cone + area of base

[tex] \fbox{Curved surface area of cylinder = 2πrh}[/tex]

= 2(3.14)(3)(12)

= 226.08 cm²

[tex]{ \fbox{Curved surface of cone = πrl}}[/tex]

= 3.14(3)(5)

= 47.1 cm²

Area of base = πr²

= (3.14)(3)²

= 3.14(9)

= 28.26 cm²

Total surface area of rocket = 226.08 + 47.1 + 28.26

= 301.44 cm²

__________________________

Hope it's helpful for you ⭐

[tex]\huge \red{ \fbox{\blue{ \fbox{follow}}{ \green{ \fbox{me}}}}} [/tex]

Answer:

Surface area of the rocket = 301.632cm²
Volume of the rocket = 716.376 cm³

Step-by-step explanation:

A. Surface area

   Cylinder                                   +                              Cone

πr²+πdh                                                                   πrl
= (3x3x3.142) + (3.142 x 6 x12)                                =3.142 x 5 x 3

=28.278cm² +  226.224cm²                                     = 47.13 cm²

=254.502cm²

Add the two

254.502cm² + 47.13 cm² = 301.632 cm²

Surface area of the rocket = 301.632cm²

B.VOLUME

Cylinder

= π r²H

H= 12cm

r= 3cm

= 3.142 x 3  x3 x 12

= 339.336 cm³

Cone

V =  1/3 π r² h

r = 3

h= ???

to find h .. use the pythagorus theorem

right angled triangle on the cone  the base is 3 cm

                                                         hypotenuse is  5cm(slant height)

                                                         the height is  unknown (h)

3² + h² = 5²

9 + h² = 25

h² = 25-9

h² = 16

h = √16

h=4cm

now we can find the volume  of the cone

=3.142 x 1/3 x 3 x 3 x 4

= 37.704cm³

Add the volume of the cone to the cylinder's

= 37.704 cm³ +339.336 cm³

Volume of the rocket = 716.376 cm³