Question

Hey!

I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.

If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.

Anyways, please show all of your work and explain your thinking! Thanks!

Answer 1

A. Cylinder + cone

Volume is the sum of volumes:

• V = Vcon + Vcyl = 1/3πr²h₁ + πr²h₂
• V = 1/3π*9²*12 + π*9²*120 = 31554.2 cm³

Surface area of cone:

• A = A=πr(r+√(h₁²+r²)) = π*9(9 + √(9²+12²)) = 678.6 cm²

Surface area of cylinder minus bases:

• A = 2πrh₂ = 2π*9*120 = 6785.8 cm²

Total surface area:

• 678.6 + 6785.8 = 7464.4 cm²

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B. Cube+ pyramid

Volume:

• V = a³ + (1/3)a²h = a³ + (1/3)a²√(l²-(a/2)²)
• V = 8³ + (1/3)8²√(10²-4²) = 707.5 cm³

Surface area of pyramid:

• A = a² + 2al = 8² + 2*8*10 = 224 cm²

Surface area of cube minus bases:

• A = 4a² = 4(8²) = 256 cm²

Total surface area:

• A = 224 + 256 = 480 cm²