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A 3 D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.

Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.

(1 point)
cubic millimeters

5 answers

To find the volume of a cylinder, you can use the formula:

\[ V = \pi r^2 h \]

where:

  • \( V \) is the volume,
  • \( r \) is the radius of the base,
  • \( h \) is the height of the cylinder.

In your case:

  • The radius \( r = 8 \) millimeters,
  • The height \( h = 13 \) millimeters.

Now, plug these values into the formula:

\[ V = \pi (8^2)(13) \]

Calculating \( 8^2 \):

\[ 8^2 = 64 \]

Now substitute this back into the volume formula:

\[ V = \pi (64)(13) \]

Calculating \( 64 \times 13 \):

\[ 64 \times 13 = 832 \]

Therefore,

\[ V = \pi (832) \]

Now, using the value of \( \pi \approx 3.14159 \):

\[ V \approx 3.14159 \times 832 \approx 2617.76 \]

Rounded to the nearest hundredth, the volume of the cylinder is:

\[ \boxed{2617.76} \text{ cubic millimeters} \]

A water bottle has a height of 16 inches and a radius of 4 inches. What is the volume, in cubic inches, of the water bottle? Use 3.14 for pi. (1 point)
cubic inches

To find the volume of a cylinder (like a water bottle), you can use the formula:

\[ V = \pi r^2 h \]

where:

  • \( V \) is the volume,
  • \( r \) is the radius of the base,
  • \( h \) is the height of the cylinder.

In this case:

  • The radius \( r = 4 \) inches,
  • The height \( h = 16 \) inches.

Substituting these values into the formula:

\[ V = 3.14 (4^2)(16) \]

Calculating \( 4^2 \):

\[ 4^2 = 16 \]

Now substitute this back into the volume formula:

\[ V = 3.14 \times 16 \times 16 \]

Calculating \( 16 \times 16 \):

\[ 16 \times 16 = 256 \]

Now substitute this back:

\[ V = 3.14 \times 256 \]

Calculating this product:

\[ V \approx 3.14 \times 256 = 804.224 \]

Thus, the volume of the water bottle is approximately:

\[ \boxed{804.22} \text{ cubic inches} \]

(rounded to the nearest hundredth).

Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches. Round your answer to the nearest hundredth. Use 3.14 for pi.(1 point)
cubic inches

To find the volume of a cone, you can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where:

  • \( V \) is the volume,
  • \( r \) is the radius of the base,
  • \( h \) is the height of the cone.

In this case:

  • The radius \( r = 13 \) inches,
  • The height \( h = 27 \) inches.

Substituting these values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (13^2) \times 27 \]

Calculating \( 13^2 \):

\[ 13^2 = 169 \]

Now substitute this into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 169 \times 27 \]

Next, calculate \( 169 \times 27 \):

\[ 169 \times 27 = 4563 \]

Now we can substitute back into the volume equation:

\[ V = \frac{1}{3} \times 3.14 \times 4563 \]

Calculating \( 3.14 \times 4563 \):

\[ 3.14 \times 4563 \approx 14368.82 \]

Now, divide by 3:

\[ V \approx \frac{14368.82}{3} \approx 4789.607 \]

Rounding to the nearest hundredth:

\[ V \approx 4789.61 \]

Thus, the volume of the cone is approximately:

\[ \boxed{4789.61} \text{ cubic inches} \]