Step 1: Recall cube surface area formula: SA = 6s² (six congruent square faces)

Step 2: Substitute s = 6: SA = 6(6)² SA = 6(36) SA = 216 cm²

Step 3: Alternative thinking: Area of one face = 6² = 36 cm² Total = 6 faces × 36 = 216 cm²

Answer: Surface area = 216 cm²

A cube has 6 congruent square faces.

$SA = 6s^2$

$SA = 6(4)^2$

$SA = 6(16)$

$SA = 96$

Answer: 96 square units

Step 1: Recall cylinder surface area formula: SA = 2πr² + 2πrh (two circular bases + lateral surface)

Step 2: Identify values: r = 5 cm, h = 12 cm

Step 3: Calculate area of two bases: 2πr² = 2π(5)² = 2π(25) = 50π cm²

Step 4: Calculate lateral (curved) surface area: 2πrh = 2π(5)(12) = 120π cm²

Step 5: Total surface area: SA = 50π + 120π SA = 170π cm²

Step 6: Approximate: SA ≈ 170 × 3.14159 ≈ 534.07 cm²

Answer: Surface area = 170π cm² (≈ 534.07 cm²)

Use $SA = 2\pi r^2 + 2\pi rh$:

$SA = 2\pi(3)^2 + 2\pi(3)(8)$

$SA = 2\pi(9) + 2\pi(24)$

$SA = 18\pi + 48\pi$

$SA = 66\pi$

Answer: $66\pi$ (or approximately 207.3) square units

Step 1: Recall the formula: SA = 2(lw + lh + wh)

Step 2: Identify dimensions: l = 8 m, w = 5 m, h = 3 m

Step 3: Calculate each face area: lw = 8 × 5 = 40 m² lh = 8 × 3 = 24 m² wh = 5 × 3 = 15 m²

Step 4: Sum and multiply by 2: SA = 2(40 + 24 + 15) SA = 2(79) SA = 158 m²

Step 5: Alternative method (6 faces): Top/Bottom: 2(8 × 5) = 80 m² Front/Back: 2(8 × 3) = 48 m² Left/Right: 2(5 × 3) = 30 m² Total: 80 + 48 + 30 = 158 m²

Answer: Surface area = 158 m²

Step 1: Recall cone surface area formula: SA = πr² + πrl where r is radius and l is slant height

Step 2: Identify values: r = 6 cm, l = 10 cm

Step 3: Calculate base area: πr² = π(6)² = 36π cm²

Step 4: Calculate lateral surface area: πrl = π(6)(10) = 60π cm²

Step 5: Total surface area: SA = 36π + 60π SA = 96π cm²

Step 6: Approximate: SA ≈ 96 × 3.14159 ≈ 301.59 cm²

Step 7: Note: If given height instead of slant height, use: l = √(r² + h²)

Answer: Surface area = 96π cm² (≈ 301.59 cm²)

Step 1: Find slant height using Pythagorean theorem

$\ell = \sqrt{r^2 + h^2}$ $\ell = \sqrt{5^2 + 12^2}$ $\ell = \sqrt{25 + 144}$ $\ell = \sqrt{169} = 13$

Step 2: Calculate surface area

$SA = \pi r^2 + \pi r\ell$ $SA = \pi(5)^2 + \pi(5)(13)$ $SA = 25\pi + 65\pi$ $SA = 90\pi$

Answer: $90\pi$ (or approximately 282.7) square units

Step 1: Recall sphere surface area formula: SA = 4πr²

Step 2: Substitute r = 7: SA = 4π(7)² SA = 4π(49) SA = 196π cm²

Step 3: Approximate: SA ≈ 196 × 3.14159 ≈ 615.75 cm²

Step 4: Interesting fact: The surface area of a sphere equals the lateral surface area of a cylinder with the same radius and height equal to the diameter (2r)

Cylinder lateral area = 2πr(2r) = 4πr² ✓

Answer: Surface area = 196π cm² (≈ 615.75 cm²)