Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel disagree on how the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?

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a) Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X

Step-by-step explanation:

From the above question, we are given two shapes: Cone W and Square Pyramid

Cone W: Radius = 8cm, Height = 5cm

Volume of a Cone = 1/3 πr²h

Where π = 3.14

Volume of Cone X = 1/3 × 3.14 × 8² × 5

= 334.93cm³

For Square pyramid X

Volume = 1/3 × Base Area × Height

Base Area of Cone W = Base Area of square pyramid X = πr²

Where π = 3.14

Base area = 3.14 × 8² = 200.96cm²

Height of Square pyramid X = Height of Cone W = 5cm

Volume of Square pyramid = 1/3 ×200.96cm² × 5cm

= 334.93cm³

Therefore, from my above calculation and compared with the arguments of Paul and Manuel, Option a) "Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X" is the correct option.

The reason why is because the correct formula for the volume of a square pyramid = 1/3 × Base area × Height

This was the formula Paul used.

Manuel on the other hand used the formula: Base Area × Height to find the volume of cone W. This formula is wrong.

Option a, is the correct answer.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

12

step-by-step explanation: