Question

puzzle one

determine the volume of the following cylinders with the given dimensions. round your answers to the hundredth place. to break the code substitute your answers in for the correct letters. make sure to follow the order of operations! use 3.14 as an approximation for pi.

a) ______

b) ______

c) ______

d) ______

code: \\((b + c) - (d + a)\\)

Explanation:

State the volume formula

To find the volume \(V\) of a cylinder, we use the formula:

$$V = \pi r^2 h$$

where \(r\) is the radius of the circular base, \(h\) is the height, and \(\pi \approx 3.14\).

Calculate Cylinder A

• Dimensions: The dashed line across the top represents the diameter \(d = 15\text{ m}\). Thus, the radius is:

$$r = \frac{15}{2} = 7.5\text{ m}$$

The height is \(h = 5.7\text{ m}\).

• Calculation:

$$V_A = 3.14 \times (7.5)^2 \times 5.7$$

$$V_A = 3.14 \times 56.25 \times 5.7 = 1006.1625\text{ m}^3$$

Rounding to the hundredth place gives \(1006.16\).

Calculate Cylinder B

• Dimensions: The dashed line across the top represents the diameter \(d = 8\text{ ft}\). Thus, the radius is:

$$r = \frac{8}{2} = 4\text{ ft}$$

The height is \(h = 14.4\text{ ft}\).

• Calculation:

$$V_B = 3.14 \times 4^2 \times 14.4$$

$$V_B = 3.14 \times 16 \times 14.4 = 723.456\text{ ft}^3$$

Rounding to the hundredth place gives \(723.46\).

Calculate Cylinder C

• Dimensions: The line from the center to the edge represents the radius \(r = 6\text{ in}\). The height is \(h = 24\text{ in}\).
• Calculation:

$$V_C = 3.14 \times 6^2 \times 24$$

$$V_C = 3.14 \times 36 \times 24 = 2712.96\text{ in}^3$$

This value is already exact to the hundredth place: \(2712.96\).

Calculate Cylinder D and the Code

• Cylinder D: The line from the center to the edge represents the radius \(r = 2\text{ in}\). The height is \(h = 8.9\text{ in}\).

$$V_D = 3.14 \times 2^2 \times 8.9$$

$$V_D = 3.14 \times 4 \times 8.9 = 111.784\text{ in}^3$$

Rounding to the hundredth place gives \(111.78\).

• Code Evaluation:

The code formula is:

$$\text{Code} = (B + C) - (D + A)$$

Substitute the rounded values:

$$\text{Code} = (723.46 + 2712.96) - (111.78 + 1006.16)$$

$$\text{Code} = 3436.42 - 1117.94 = 2318.48$$

Answer:

No.	Problem	Answer
B	Volume of Cylinder B	\(723.46\text{ ft}^3\)
C	Volume of Cylinder C	\(2712.96\text{ in}^3\)
D	Volume of Cylinder D	\(111.78\text{ in}^3\)
Code	\((B + C) - (D + A)\)	\(2318.48\)