Find volume and surface area of 10 geometric figures with given dimensions.

Let’s solve each problem step by step. We’ll find the volume and surface area for each rectangular prism (or cube).

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🔢 Formulas we’ll use:

For a rectangular prism with length = l, width = w, height = h:

- Volume = l × w × h
- Surface Area = 2(lw + lh + wh)

For a cube (all sides equal), if side = s:

- Volume = s³
- Surface Area = 6s²

We’ll go one by one.

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## Problem 1:
Dimensions: 7 cm × 40 cm × 48 cm

→ Volume = 7 × 40 × 48
First: 7 × 40 = 280
Then: 280 × 48
Break it down: 280 × 50 = 14,000 → minus 280 × 2 = 560 → 14,000 - 560 = 13,440 cm³

→ Surface Area = 2[(7×40) + (7×48) + (40×48)]
Calculate inside:
7×40 = 280
7×48 = 336
40×48 = 1920
Sum = 280 + 336 + 1920 = 2536
Multiply by 2 → 5072 cm²

✔ Answer 1: Volume = 13,440 cm³, Surface Area = 5072 cm²

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## Problem 2:
Dimensions: 27 cm × 41 cm × 34 cm

→ Volume = 27 × 41 × 34
First: 27 × 41
27 × 40 = 1080, plus 27 × 1 = 27 → 1107
Then: 1107 × 34
Break it: 1107 × 30 = 33,210; 1107 × 4 = 4,428
Add: 33,210 + 4,428 = 37,638 cm³

→ Surface Area = 2[(27×41) + (27×34) + (41×34)]
Calculate:
27×41 = 1107
27×34 = 918
41×34 = 1394
Sum = 1107 + 918 + 1394 = 3419
Multiply by 2 → 6838 cm²

✔ Answer 2: Volume = 37,638 cm³, Surface Area = 6838 cm²

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## Problem 3:
Cube: 20 cm on each side

→ Volume = 20³ = 20 × 20 × 20 = 400 × 20 = 8000 cm³

→ Surface Area = 6 × (20²) = 6 × 400 = 2400 cm²

✔ Answer 3: Volume = 8000 cm³, Surface Area = 2400 cm²

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## Problem 4:
Dimensions: 42 cm × 25 cm × 25 cm

→ Volume = 42 × 25 × 25
First: 25 × 25 = 625
Then: 42 × 625
Break it: 40 × 625 = 25,000; 2 × 625 = 1,250 → total = 26,250 cm³

→ Surface Area = 2[(42×25) + (42×25) + (25×25)]
Note: two faces are same (42×25)
So: 42×25 = 1050 → appears twice → 2100
25×25 = 625
Sum = 2100 + 625 = 2725
Multiply by 2 → 5450 cm²

Wait — let me double-check formula:
It’s 2(lw + lh + wh)
l=42, w=25, h=25
lw = 42×25 = 1050
lh = 42×25 = 1050
wh = 25×25 = 625
Sum = 1050 + 1050 + 625 = 2725
×2 = 5450 cm² ✔

✔ Answer 4: Volume = 26,250 cm³, Surface Area = 5450 cm²

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## Problem 5:
Dimensions: 18 cm × 3 cm × 24 cm

→ Volume = 18 × 3 × 24
First: 18 × 3 = 54
Then: 54 × 24
50×24=1200, 4×24=96 → 1200+96=1296 cm³

→ Surface Area = 2[(18×3) + (18×24) + (3×24)]
Calculate:
18×3 = 54
18×24 = 432
3×24 = 72
Sum = 54 + 432 + 72 = 558
×2 = 1116 cm²

✔ Answer 5: Volume = 1296 cm³, Surface Area = 1116 cm²

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## Problem 6:
Cube: 25 cm on each side

→ Volume = 25³ = 25 × 25 × 25 = 625 × 25
600×25=15,000; 25×25=625 → total = 15,625 cm³

→ Surface Area = 6 × (25²) = 6 × 625 = 3750 cm²

✔ Answer 6: Volume = 15,625 cm³, Surface Area = 3750 cm²

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## Problem 7:
Dimensions: 20 cm × 33 cm × 23 cm

→ Volume = 20 × 33 × 23
First: 20 × 33 = 660
Then: 660 × 23
660 × 20 = 13,200; 660 × 3 = 1,980 → total = 15,180 cm³

→ Surface Area = 2[(20×33) + (20×23) + (33×23)]
Calculate:
20×33 = 660
20×23 = 460
33×23 = 759 (since 30×23=690, 3×23=69 → 690+69=759)
Sum = 660 + 460 + 759 = 1879
×2 = 3758 cm²

✔ Answer 7: Volume = 15,180 cm³, Surface Area = 3758 cm²

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## Problem 8:
Dimensions: 45 cm × 6 cm × 14 cm

→ Volume = 45 × 6 × 14
First: 45 × 6 = 270
Then: 270 × 14
270 × 10 = 2700; 270 × 4 = 1080 → total = 3780 cm³

→ Surface Area = 2[(45×6) + (45×14) + (6×14)]
Calculate:
45×6 = 270
45×14 = 630 (45×10=450, 45×4=180 → 450+180=630)
6×14 = 84
Sum = 270 + 630 + 84 = 984
×2 = 1968 cm²

✔ Answer 8: Volume = 3780 cm³, Surface Area = 1968 cm²

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## Problem 9:
Dimensions: 14 cm × 48 cm × 22 cm

→ Volume = 14 × 48 × 22
First: 14 × 48
10×48=480, 4×48=192 → 480+192=672
Then: 672 × 22
672 × 20 = 13,440; 672 × 2 = 1,344 → total = 14,784 cm³

→ Surface Area = 2[(14×48) + (14×22) + (48×22)]
Calculate:
14×48 = 672
14×22 = 308
48×22 = 1056 (50×22=1100 minus 2×22=44 → 1100-44=1056)
Sum = 672 + 308 + 1056 = 2036
×2 = 4072 cm²

✔ Answer 9: Volume = 14,784 cm³, Surface Area = 4072 cm²

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## Problem 10:
Cube: 22 cm on each side

→ Volume = 22³ = 22 × 22 × 22
22×22 = 484
484 × 22
484 × 20 = 9,680; 484 × 2 = 968 → total = 10,648 cm³

→ Surface Area = 6 × (22²) = 6 × 484
6 × 400 = 2400; 6 × 84 = 504 → 2400 + 504 = 2904 cm²

✔ Answer 10: Volume = 10,648 cm³, Surface Area = 2904 cm²

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Final Answer:

1) Volume = 13,440 cm³, Surface Area = 5072 cm²
2) Volume = 37,638 cm³, Surface Area = 6838 cm²
3) Volume = 8000 cm³, Surface Area = 2400 cm²
4) Volume = 26,250 cm³, Surface Area = 5450 cm²
5) Volume = 1296 cm³, Surface Area = 1116 cm²
6) Volume = 15,625 cm³, Surface Area = 3750 cm²
7) Volume = 15,180 cm³, Surface Area = 3758 cm²
8) Volume = 3780 cm³, Surface Area = 1968 cm²
9) Volume = 14,784 cm³, Surface Area = 4072 cm²
10) Volume = 10,648 cm³, Surface Area = 2904 cm²