Example Question - cone formula
Here are examples of questions we've helped users solve.
Calculating the Volume of a Cone with Given Parameters
The photo is unclear, but it seems to show geometric formulas related to a cone. You've provided parameters for a cone: the radius (r) is 2 cm, and the height (h) is 4 cm. Assuming you want to find the volume of the cone, here is how you can calculate it using the given values: The volume (V) of a cone can be found using the formula: V = (1/3) * π * r^2 * h Plugging in the given values: r = 2 cm h = 4 cm V = (1/3) * π * (2 cm)^2 * 4 cm V = (1/3) * π * 4 cm^2 * 4 cm V = (1/3) * π * 16 cm^3 V = (16/3) * π cm^3 To get a numerical value, multiply (16/3) by the approximate value of π (3.14159265359): V ≈ (16/3) * 3.14159 cm^3 V ≈ 16.75516 cm^3 So the approximate volume of the cone is 16.75516 cubic centimeters. If you need the exact value, keep π in the calculation and the volume is (16/3)π cm³.
Calculating Cone Radius With Given Volume and Height
To find the radius of the cone, we can use the formula for the volume of a cone: \[ V = \frac{1}{3}\pi r^2 h \] Where: - \( V \) is the volume of the cone, - \( r \) is the radius of the base of the cone, - \( h \) is the height of the cone, - \( \pi \) is approximately 3.14 (given). The volume (\( V \)) is given as 37.68 cubic millimeters, and the height (\( h \)) is given as 4 millimeters. To find \( r \), we can rearrange the formula to solve for \( r^2 \): \[ r^2 = \frac{3V}{\pi h} \] Now we'll use the given values: \[ r^2 = \frac{3 \times 37.68}{3.14 \times 4} \] First, let's calculate the numerator of the fraction: \[ 3 \times 37.68 = 113.04 \] And the denominator of the fraction: \[ 3.14 \times 4 = 12.56 \] Next, we'll divide these two results to find \( r^2 \): \[ r^2 = \frac{113.04}{12.56} \approx 9 \] Now take the square root of 9 to find the radius \( r \): \[ r = \sqrt{9} = 3 \] So the radius \( r \) of the cone is 3 millimeters. Since the problem asks to round our answer to the nearest hundredth, our final answer in two decimal places would still be: \[ r \approx 3.00 \text{ millimeters} \]
Calculating Volume of a Cone
The question in the image is asking for the volume of a cone. The formula to calculate the volume of a cone is: \[ \text{Volume} = \frac{1}{3} \pi r^2 h \] where \( \pi \) is Pi, approximately 3.14159, \( r \) is the radius of the base of the cone, and \( h \) is the height of the cone. According to the image, the ice cream cone has a diameter of 3 inches, which means the radius \( r \) is half of that, so \( r = 1.5 \) inches. The height \( h \) of the cone is given as 7 inches. Now plug these values into the formula to find the volume: \[ \text{Volume} = \frac{1}{3} \pi (1.5)^2 \cdot 7 \] \[ \text{Volume} = \frac{1}{3} \pi \cdot 2.25 \cdot 7 \] \[ \text{Volume} = \frac{1}{3} \cdot 3.14159 \cdot 2.25 \cdot 7 \] \[ \text{Volume} = \frac{1}{3} \cdot 3.14159 \cdot 15.75 \] \[ \text{Volume} = 3.14159 \cdot 5.25 \] \[ \text{Volume} = 16.49351 \cdot 3 \] \[ \text{Volume} = 49.480525 \text{ in}^3 \] Rounded to the nearest tenth, the volume is approximately 49.5 cubic inches. Based on the answer choices provided in the image, none of them match this exact answer. It might be a good idea to double-check the calculations or see if the image contains any error in the question or answer options.
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