Find the surface area of this composite figure to the nearest hundredth.

Question

Find the surface area of this composite figure to the nearest hundredth.

https://ibb.co/HTQYrwVc

Answer 1

To solve this, we break the composite figure into two parts: a rectangular prism and a cylinder sitting on top.

1. Surface Area of the Rectangular Prism

Dimensions: 4 cm × 4 cm × 2 cm

Formula: SA = 2(lw + lh + wh)

= 2(4×4 + 4×2 + 4×2)

= 2(16 + 8 + 8) = 2(32) = 64 cm²

Since the cylinder is sitting on top, we subtract the area of the circular hole:

Area of hole: πr² = π(1)² ≈ 3.14 cm²

Adjusted prism area:

64 − 3.14 = 60.86 cm²

2. Surface Area of the Cylinder

Radius: 1 cm Height: 8 cm

We include only the lateral surface and the top circle (not the bottom since it’s attached to the prism).

Lateral area: 2πrh = 2π(1)(8) = 16π ≈ 50.27 cm²

Top circle: πr² = π(1)² ≈ 3.14 cm²

Total cylinder area:

50.27 + 3.14 = 53.41 cm²

Final Surface Area:

60.86 + 53.41 = 114.27 cm²

Let me know if you’d like help visualizing or solving more composite geometry problems!

Best regards,

Sid Bhatia

Answer 2

1) Surface Area of a cylinder is equal to the two circular ends (top and bottom) as well as the side. If you think of a cylinder as a roll of paper towels, unwrapping the first layer yields a section of paper towels which is a rectangle, as tall as the roll (H) and long enough to wrap all the way around the circumference of the cylinder (L = C = 2 pi r). So,

S = 2 (pi r²) + 2 pi r H = 2 pi r (r+H)

2) Surface area of a rectangular prism (cube like box) is equal to all 6 faces, front and back, left and right, top and bottom. Due to its symmetry, each pair of opposite faces is the exact same size. Thus,

S = 2 (L x W) + 2 (W x H) + 2 (H x L) = 2 (LW + WH + HL)

3) Combining the figures while removing the bottom circular end of the cylinder also requires removing an equal circular section to create the opening into the rectangular prism. Therefore,

S = 2 pi r (r+H) + 2 (LxW + WxH + HxL) - 2 (pi r²) = 2 pi r (H) + 2(LW + WH + HL)

= 2 pi 1 (8 - 2) + 2 (4x4 + 4x2 + 2x4) = 64 + 12 pi ≈101.70 (to the nearest hundredth)