What is the volume of the cone in cubic centimeters? Round your answer to the nearest tenth.(1 point) cubic centimeters
Radie's= 5cm
Length= 9cm
the raidus is 5 the height is 9
the answer is 235.5 this bot is just slow
pi = 5 x 5 x 9 = 225
225 divided by 3 = 75
75 x 3.14 = 235.5
Wrong
What is the volume, in cubic millimeters, of the cone? Round your answer to the nearest hundredth.(1 point) cubic millimeters
raides=14mm
length=12mm
Apologies for the confusion in my initial response. Let's try calculating the volume of the cone again using the correct height.
You have provided the radius \( r = 5 \) cm, but you've mentioned the "length" as 9 cm. Without further clarification, I will assume that by "length," you meant the vertical height \( h \) of the cone, since the slant height would typically not be used to calculate the volume.
Given:
- Radius \( r = 5 \) cm
- Height \( h = 9 \) cm
Using the formula for the volume of a cone:
\[ V = \frac{1}{3}\pi r^2 h \]
Plugging in the given values:
\[ V = \frac{1}{3} \pi \times (5 \text{ cm})^2 \times 9 \text{ cm} \]
\[ V = \frac{1}{3} \pi \times 25 \text{ cm}^2 \times 9 \text{ cm} \]
\[ V = \frac{1}{3} \times 3.14159 \times 225 \text{ cm}^2 \]
\[ V = \frac{1}{3} \times 3.14159 \times 225 \times 9 \]
\[ V = 3.14159 \times 75 \times 9 \]
\[ V = 3.14159 \times 675 \]
\[ V \approx 2119.86225 \]
Rounding to the nearest tenth:
\[ V \approx 2119.9 \text{ cm}^3 \]
So the volume of the cone is approximately \( 2119.9 \) cubic centimeters.
To find the volume of a cone, you can use the formula:
V = (1/3) * π * r^2 * h
Where:
V is the volume of the cone,
r is the radius of the cone's base, and
h is the height or length of the cone.
In this case, the radius (r) is given as 5 cm, and the length or height (h) is given as 9 cm. We can substitute these values into the formula:
V = (1/3) * π * 5^2 * 9
Simplifying this expression:
V = (1/3) * π * 25 * 9
V = (1/3) * π * 225
To round the answer to the nearest tenth, we need to calculate the actual value of the volume using the value of π:
V ≈ (1/3) * 3.14 * 225
Calculating this:
V ≈ 75.0
So, the volume of the cone is approximately 75.0 cubic centimeters when rounded to the nearest tenth.
To find the volume of a cone, you can use the following formula:
\[ V = \frac{1}{3}\pi r^2 h \]
Here, \( V \) is the volume of the cone, \( r \) is the radius, and \( h \) is the height of the cone.
Given that the radius \( r \) is 5 cm, and the slant height (length) \( l \) is 9 cm, we cannot directly use the slant height in this volume formula. We need the vertical height \( h \) of the cone. The vertical height can be determined by using the Pythagorean theorem since the radius, slant height, and height form a right-angled triangle.
Let's calculate the height \( h \) with the Pythagorean theorem:
\[ h = \sqrt{l^2 - r^2} \]
\[ h = \sqrt{9^2 - 5^2} \]
\[ h = \sqrt{81 - 25} \]
\[ h = \sqrt{56} \]
\[ h = 7.483 \text{ cm} \]
Now that we have the height, we can calculate the volume:
\[ V = \frac{1}{3} \pi (5 \text{ cm})^2 (7.483 \text{ cm}) \]
\[ V = \frac{1}{3} \pi \cdot 25 \text{ cm}^2 \cdot 7.483 \text{ cm} \]
\[ V = \frac{1}{3} \cdot 3.14159 \cdot 25 \cdot 7.483 \]
\[ V \approx \frac{1}{3} \cdot 3.14159 \cdot 187.075 \]
\[ V \approx 196.349 \text{ cm}^3 (before rounding) \]
Rounded to the nearest tenth:
\[ V \approx 196.3 \text{ cm}^3 \]
Therefore, the volume of the cone is approximately 196.3 cubic centimeters.
To find the volume of a cone using the given radius, we first need to determine the height of the cone, as the given "length" likely refers to the slant height. To solve for the height, we can use the Pythagorean theorem since the radius (r), slant height (l), and height (h) of a right circular cone form a right triangle.
Given:
Radius (r) = 14 mm
Slant height (l) = 12 mm
To find the height (h) of the cone, we can use the formula:
\( h = \sqrt{l^2 - r^2} \)
Solving for h:
\( h = \sqrt{12^2 - 14^2} \)
This cannot be correct because the slant height must be greater than the radius for a real right circular cone. We seem to have a mistake in our interpretation of the given "length." If instead, you meant the "length" as the vertical height, let's proceed with the volume calculation using that as the height of the cone.
Assuming the "length" is the vertical height (h):
Height (h) = 12 mm
Now, we can calculate the volume (V) using the cone volume formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Substituting the given values:
\[ V = \frac{1}{3} \pi (14 \, \text{mm})^2 (12 \, \text{mm}) \]
\[ V = \frac{1}{3} \pi 196 \, \text{mm}^2 (12 \, \text{mm}) \]
\[ V = \frac{1}{3} \pi 2352 \, \text{mm}^3 \]
\[ V = 784 \, \text{mm}^3 \pi \]
\[ V \approx 784 \times 3.14159 \, \text{mm}^3 \]
\[ V \approx 2463.01196 \, \text{mm}^3 \]
Rounding to the nearest hundredth, the volume is:
\[ V \approx 2463.01 \, \text{mm}^3 \]
So the volume of the cone is approximately 2463.01 cubic millimeters.