Question

calculator
what is the volume of this solid?
use 3.14 for pi.
37.68 cm³
138.16 cm³
169.56 cm³
207.24 cm³

Explanation:

Step1: Find volume of cylinder

The formula for the volume of a cylinder is $V_{cylinder} = \pi r^2 h$. Given $r = 3$ cm, $h = 6$ cm, and $\pi = 3.14$.
$V_{cylinder} = 3.14\times3^2\times6 = 3.14\times9\times6 = 169.56$ $cm^3$.

Step2: Find volume of cone

The formula for the volume of a cone is $V_{cone} = \frac{1}{3}\pi r^2 h$. Given $r = 3$ cm, $h = 4$ cm, and $\pi = 3.14$.
$V_{cone} = \frac{1}{3}\times3.14\times3^2\times4 = \frac{1}{3}\times3.14\times9\times4 = 37.68$ $cm^3$.

Step3: Find total volume

Add the volume of the cylinder and the cone.
$V_{total} = V_{cylinder} + V_{cone} = 169.56 + 37.68 = 207.24$ $cm^3$? Wait, no, wait. Wait, let's recalculate. Wait, no, maybe I made a mistake. Wait, no, wait the options: wait 169.56 + 37.68 is 207.24? But let's check again. Wait, no, wait the cylinder: $3.14*9*6 = 169.56$. Cone: $\frac{1}{3}*3.14*9*4 = 37.68$. Then total is 169.56 + 37.68 = 207.24? But wait the options have 207.24 as an option. Wait, but let me check the problem again. Wait, the solid is a cylinder and a cone on top. So radius is 3, cylinder height 6, cone height 4. So yes, cylinder volume: $πr²h = 3.14*9*6 = 169.56$. Cone volume: (1/3)πr²h = (1/3)3.149*4 = 37.68. Total volume: 169.56 + 37.68 = 207.24 $cm^3$. Wait, but let me check the options. The last option is 207.24 $cm^3$. So that's the answer.

Wait, but wait, maybe I miscalculated. Wait, 3^2 is 9, 96 is 54, 543.14 is 169.56. Then cone: 94 is 36, 363.14 is 113.04, divided by 3 is 37.68. Then 169.56 + 37.68 is 207.24. Yes. So the total volume is 207.24 $cm^3$.

Answer:

207.24 $cm^3$ (Option: 207.24 $cm^3$)