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sesenic [268]
3 years ago
5

Can someone find the surface area of the composite shape and show work! I’ll give 30pts! Thanks!

Mathematics
1 answer:
aivan3 [116]3 years ago
8 0

Answer:

382 cm²

Step-by-step explanation:

The shape can be decomposed into two rectangular prism or cuboids

✔️Dimension of prism 1 (smaller prism):

L = 10 cm

W = 3 cm

H = 7 - 4 = 3 cm

Surface area of prism 1 = 2(LW + LH + WH)

= 2(10*3 + 10*3 + 3*3)

= 2(69)

Surface area of prism 1 = 138 cm²

✔️Dimension of prism 2 (larger prism):

L = 10 cm

W = 8 cm

H = 4 cm

Surface area of prism = 2(LW + LH + WH)

= 2(10*8 + 10*4 + 8*4)

= 2(152)

Surface area of prism 2 = 304 cm²

✅Surface Area of the composite shape = (Surface area of prism 1 + surface area of prism 2) - (2 × area of the base of prism 1)

= (138 + 304) - (2 × L × W)

= 442 - (2 × 10 × 3)

= 442 - 60

= 382 cm²

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3,628,800 ways can they arrange themselves in the shuttle, If 10 friends are going to occupy 10 seats in shuttle on the way to the airport.

Step-by-step explanation:

The given is,

                   10 friends are going to occupy 10 seats in shuttle on the way to the airport  

Step:1

                   No. of friends - 10

                   No.of seats in space shuttle - 10

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                                       P_{n} = n!............................(1)

                    Where, n - Positive integer

Step:2

                  From given, n = 10                  

                  Equation (1) becomes,

                                     P_{10} = 10!

                                            = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

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                                            = 3628800 ways

Result:

                3,628,800 ways can they arrange themselves in the shuttle, If 10 friends are going to occupy 10 seats in shuttle on the way to the airport.

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