What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth

Question

What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth
r(5 cm)   h(9 cm)

GPT-4o mini · Accepted Answer

To find the volume $ V $ of a cone, you can use the formula: $$ V = \frac{1}{3} \pi r^2 h $$ where: - $ r $ is the radius of the base of the cone, - $ h $ is the height of the cone. In your case, the radius $ r $ is 5 cm and the height $ h $ is 9 cm. Using $ \pi \approx 3.14 $: 1. Calculate $ r^2 $: $$ r^2 = 5^2 = 25 $$ 2. Substitute the values into the volume formula: $$ V = \frac{1}{3} \times 3.14 \times 25 \times 9 $$ 3. Calculate $ 3.14 \times 25 $: $$ 3.14 \times 25 = 78.5 $$ 4. Now multiply that result by 9: $$ 78.5 \times 9 = 706.5 $$ 5. Finally, divide by 3: $$ V = \frac{706.5}{3} \approx 235.5 $$ So, the volume of the cone is approximately **235.5 cubic centimeters** when rounded to the nearest tenth.

dino scientist · Answer

What is the volume, in cubic inches, of a cone with a diameter of 6 inches and a height of 7 inches? Use 3.14 for pi. Round your answer to the nearest hundredth

GPT-4o mini · Answer

To find the volume $ V $ of a cone, we use the formula: $$ V = \frac{1}{3} \pi r^2 h $$ where: - $ r $ is the radius of the base of the cone, - $ h $ is the height of the cone. Given: - The diameter of the cone is 6 inches, so the radius $ r $ is half of that: $$ r = \frac{6}{2} = 3 \text{ inches} $$ - The height $ h $ is 7 inches. Now, we can calculate the volume: 1. Calculate $ r^2 $: $$ r^2 = 3^2 = 9 $$ 2. Substitute the values into the volume formula: $$ V = \frac{1}{3} \times 3.14 \times 9 \times 7 $$ 3. First, calculate $ 9 \times 7 $: $$ 9 \times 7 = 63 $$ 4. Now substitute this back into the formula: $$ V = \frac{1}{3} \times 3.14 \times 63 $$ 5. Calculate $ 3.14 \times 63 $: $$ 3.14 \times 63 = 197.82 $$ 6. Finally, divide by 3 to find the volume: $$ V = \frac{197.82}{3} \approx 65.94 $$ Thus, the volume of the cone is approximately **65.94 cubic inches** when rounded to the nearest hundredth.

dino scientist · Answer

What is the volume, in cubic millimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth r(7 mm) h(12 mm)

GPT-4o mini · Answer

To find the volume $ V $ of a cone, we use the formula: $$ V = \frac{1}{3} \pi r^2 h $$ where: - $ r $ is the radius of the base of the cone, - $ h $ is the height of the cone. In your case, the values are: - $ r = 7 $ mm - $ h = 12 $ mm Now, we can calculate the volume: 1. Calculate $ r^2 $: $$ r^2 = 7^2 = 49 $$ 2. Substitute the values into the volume formula: $$ V = \frac{1}{3} \times 3.14 \times 49 \times 12 $$ 3. First, calculate $ 49 \times 12 $: $$ 49 \times 12 = 588 $$ 4. Now substitute this back into the formula: $$ V = \frac{1}{3} \times 3.14 \times 588 $$ 5. Calculate $ 3.14 \times 588 $: $$ 3.14 \times 588 = 1847.92 $$ 6. Finally, divide by 3 to find the volume: $$ V = \frac{1847.92}{3} \approx 615.97 $$ Thus, the volume of the cone is approximately **615.97 cubic millimeters** when rounded to the nearest hundredth.

dino scientist · Answer

A coffee maker has a cone-shaped container to hold the coffee grounds. The radius of the container is 3 inches and the height is 7 inches. What is the volume, in cubic inches, of coffee grounds the container can hold? Round your answer to the nearest hundredth and use 3.14 for π

GPT-4o mini · Answer

To find the volume $ V $ of a cone-shaped container, we use the formula: $$ V = \frac{1}{3} \pi r^2 h $$ where: - $ r $ is the radius of the base, - $ h $ is the height. In your case: - The radius $ r = 3 $ inches, - The height $ h = 7 $ inches. Now, let's calculate the volume. 1. Calculate $ r^2 $: $$ r^2 = 3^2 = 9 $$ 2. Plug in the values into the volume formula: $$ V = \frac{1}{3} \times 3.14 \times 9 \times 7 $$ 3. First, calculate $ 9 \times 7 $: $$ 9 \times 7 = 63 $$ 4. Now substitute this back into the formula: $$ V = \frac{1}{3} \times 3.14 \times 63 $$ 5. Calculate $ 3.14 \times 63 $: $$ 3.14 \times 63 = 197.82 $$ 6. Finally, divide by 3 to find the volume: $$ V = \frac{197.82}{3} \approx 65.94 $$ Thus, the volume of the cone-shaped container is approximately **65.94 cubic inches** when rounded to the nearest hundredth.

dino scientist · Answer

A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π

GPT-4o mini · Answer

To find the volume $ V $ of a cone (the shape of the water tank), we can use the formula: $$ V = \frac{1}{3} \pi r^2 h $$ where: - $ r $ is the radius of the base of the cone, - $ h $ is the height of the cone. Given: - The diameter of the tank is 12 feet, so the radius $ r $ is half of that: $$ r = \frac{12}{2} = 6 \text{ feet} $$ - The height $ h $ is 15 feet. Now we can calculate the volume: 1. Calculate $ r^2 $: $$ r^2 = 6^2 = 36 $$ 2. Substitute the values into the volume formula: $$ V = \frac{1}{3} \times 3.14 \times 36 \times 15 $$ 3. First, calculate $ 36 \times 15 $: $$ 36 \times 15 = 540 $$ 4. Now substitute this back into the formula: $$ V = \frac{1}{3} \times 3.14 \times 540 $$ 5. Calculate $ 3.14 \times 540 $: $$ 3.14 \times 540 = 1695.6 $$ 6. Finally, divide by 3 to find the volume: $$ V = \frac{1695.6}{3} \approx 565.2 $$ Thus, the volume of the cone-shaped water tank is approximately **565.2 cubic feet** when rounded to the nearest tenth.