Question

directions: find the volume of each figure. round to the nearest hundredth when necessary. 1. 14 in 17.5 in 6.4 in 3. 13 mm 19 mm 5. 18 ft 25 ft 7 ft 7. 11 m 16 m 9.5 m 14 m 12.7 m

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 of first rectangular - prism

For the first rectangular - prism with $l = 17.5$ in, $w = 14$ in, and $h = 6.4$ in, we have $V_1=17.5\times14\times6.4 = 17.5\times89.6 = 1576$ 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 $d = 13$ mm, so $r=\frac{13}{2}=6.5$ mm and $h = 19$ mm. Then $V_2=\pi\times(6.5)^{2}\times19=\pi\times42.25\times19 = 802.75\pi\approx802.75\times3.14159\approx2521.99$ mm³.

Step4: Calculate volume of second rectangular - prism

For the second rectangular - prism with $l = 18$ ft, $w = 25$ ft, and $h = 7$ ft, $V_3=18\times25\times7=18\times175 = 3150$ ft³.

Step5: Calculate volume of third rectangular - prism

For the third rectangular - prism with $l = 16$ m, $w = 9.5$ m, and $h = 14$ m, $V_4=16\times9.5\times14=16\times133 = 2128$ m³.

Answer:

First figure: 1576 in³
Second figure: approximately 2521.99 mm³
Third figure: 3150 ft³
Fourth figure: 2128 m³