Question

a cone has a height of 7 meters and a diameter of 14 meters. what is its volume? round your answer to the nearest hundredth. 179.51 359.01 89.75 538.52 what is the volume of this cone? round your answer to the nearest hundredth. (image of a cone with height 17 in and radius 14 in) 1743.75 6974.98 435.94 3487.49

Explanation:

First Cone Problem (Height = 7 m, Diameter = 14 m)

Step 1: Find the radius

The diameter is 14 meters, so the radius \( r = \frac{14}{2} = 7 \) meters.

Step 2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step 3: Substitute the values

Substitute \( r = 7 \) m and \( h = 7 \) m into the formula:

$$ V = \frac{1}{3} \pi (7)^2 (7) $$

$$ V = \frac{1}{3} \pi (49)(7) $$

$$ V = \frac{343}{3} \pi \approx \frac{343}{3} \times 3.14159 $$

$$ V \approx 114.3333 \times 3.14159 \approx 359.01 $$

Step 1: Recall the volume formula for a cone

The volume \( V \) of a cone is \( V = \frac{1}{3}\pi r^2 h \), where \( r = 14 \) in and \( h = 17 \) in.

Step 2: Substitute the values

$$ V = \frac{1}{3} \pi (14)^2 (17) $$

$$ V = \frac{1}{3} \pi (196)(17) $$

$$ V = \frac{3332}{3} \pi \approx \frac{3332}{3} \times 3.14159 $$

$$ V \approx 1110.6667 \times 3.14159 \approx 3487.49 $$

Wait, looking at the options, the last option is 3,487.49 (probably a typo in the image as 3,487.49). Let's check again. Wait, maybe I misread the radius. Wait the diagram: the radius is 14 in? Wait the diagram shows 14 in as the radius? Wait the height is 17 in. Wait let's recalculate:

Wait \( r = 14 \), \( h = 17 \)

\( V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (14)^2 (17) = \frac{1}{3} \pi (196)(17) = \frac{3332}{3} \pi \approx 3332 \times 1.0472 \approx 3332 \times 1.0472 \approx 3487.49 \), which matches the last option (3,487.49, probably a comma as thousand separator).

Answer:

B. 359.01

Second Cone Problem (Radius = 14 in, Height = 17 in)