Question

directions: find the volume of each figure. round to the nearest hundredth when necessary. 1. 3. 5. 7.

Explanation:

Step1: Recall volume formula for rectangular - prism

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Calculate volume for first rectangular - prism

For the first rectangular - prism with $l = 17.5$ in, $w = 6.4$ in, and $h = 4$ in, we have $V_1=17.5\times6.4\times4$.
$V_1 = 17.5\times25.6 = 448.00$ in³.

Step3: Recall volume formula for cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Given diameter $d = 13$ mm, so $r=\frac{13}{2}=6.5$ mm and $h = 19$ mm. Then $V_2=\pi\times(6.5)^{2}\times19$.
$V_2=\pi\times42.25\times19\approx3.14\times42.25\times19 = 3.14\times802.75=2520.64$ mm³.

Step4: Calculate volume for third rectangular - prism

For the third rectangular - prism with $l = 18$ ft, $w = 7$ ft, and $h = 25$ ft, $V_3=18\times7\times25$.
$V_3 = 18\times175=3150.00$ ft³.

Step5: Calculate volume for fourth rectangular - prism

For the fourth rectangular - prism with $l = 16$ m, $w = 9.5$ m, and $h = 14$ m, $V_4=16\times9.5\times14$.
$V_4 = 16\times133 = 2128.00$ m³.

Answer:

1. $448.00$ in³
2. $2520.64$ mm³
3. $3150.00$ ft³
4. $2128.00$ m³