Show the steps taken to complete the problems:

volume of a cylinder: 34m diameter and 27m height
use 3.14 for pi.

find the surface area of the cone. 8in. diameter and 7in. height.

find the lateral area of the square pyramid: 8in. base and 22in. slant

Volume cylinder = 24501.42 m³

The surface area of the cone = 151.5 in²

The lateral area of the square pyramid = 352 in²

Step-by-step explanation:

∵ The volume of the cylinder = area base × height

∵ Its base is a circle

∴ V = πr² × h = 3.14 × (34/2)² × 27 = 24501.42 m³

∵ The surface area of the cone = 1/2 perimeter base ×  Slant height + area base

∵ Its base is a circle

∴ S.A = (1/2) × 2πr × l + πr²

∵ The slant height =

∴ S.A = 3.14 × (8/2) × √65 + 3.14 × (8/2)² = 151.5 in²

∵ The lateral area of the square pyramid = 1/2 perimeter base × slant height

∵ Its base is a square

∴ L.A = 1/2 × (8 × 4) × 22 = 352 in²

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step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.