Question

find the perimeter (or circumference) and area of the given shape. round to the nearest tenth if necessary.

1. find the perimeter (or circumference) and area of the given shape. round to the nearest tenth if necessary.

141.
142.
143.
find the surface area and volume of the given figure. round to the nearest tenth if necessary.
144.
145.
146.
147.

Explanation:

Step1: Solve for 140 (trapezoid)

Perimeter: Add all side - lengths. $P = 15 + 5+9 + 5=34$ cm. Area: Use formula $A=\frac{(a + b)h}{2}$, where $a = 15$ cm, $b = 9$ cm, $h = 4$ cm. $A=\frac{(15 + 9)\times4}{2}=\frac{24\times4}{2}=48$ $cm^{2}$.

Step2: Solve for 141 (circle)

Circumference: Use formula $C = 2\pi r$, with $r=\frac{23}{2}$ mm. $C = 2\pi\times\frac{23}{2}=23\pi\approx72.3$ mm. Area: Use formula $A=\pi r^{2}$, $A=\pi\times(\frac{23}{2})^{2}=\frac{529\pi}{4}\approx415.5$ $mm^{2}$.

Step3: Solve for 142 (composite - shape)

Perimeter: Add all outer side - lengths. $P=6 + 5+2+(6 - 3)+3+(5 - 2)=22$ in. Area: Split into two rectangles. One with dimensions $3\times6$ and the other $2\times(5 - 3)$. $A=(3\times6)+(2\times2)=18 + 4 = 22$ $in^{2}$.

Step4: Solve for 143 (composite - shape)

Perimeter: Add straight - lengths and half - circle length. $C = 14+10+10+\pi\times\frac{10}{2}=34 + 5\pi\approx49.7$ m. Area: Add rectangle and half - circle areas. $A=(14\times10)+\frac{1}{2}\pi\times(\frac{10}{2})^{2}=140+\frac{25\pi}{2}\approx179.3$ $m^{2}$.

Step5: Solve for 144 (cube)

Surface area: Use formula $SA = 6s^{2}$, with $s = 8$ cm. $SA=6\times8^{2}=384$ $cm^{2}$. Volume: Use formula $V=s^{3}$, $V = 8^{3}=512$ $cm^{3}$.

Step6: Solve for 145 (rectangular prism)

Surface area: Use formula $SA=2(lw+lh+wh)$, with $l = 12$ in, $w = 2$ in, $h = 3$ in. $SA=2(12\times2+12\times3+2\times3)=2(24 + 36+6)=132$ $in^{2}$. Volume: Use formula $V=lwh$, $V=12\times2\times3 = 72$ $in^{3}$.

Step7: Solve for 146 (cylinder)

Surface area: Use formula $SA = 2\pi r(r + h)$, with $r = 7$ cm, $h = 3$ cm. $SA=2\pi\times7(7 + 3)=140\pi\approx439.8$ $cm^{2}$. Volume: Use formula $V=\pi r^{2}h$, $V=\pi\times7^{2}\times3=147\pi\approx461.8$ $cm^{3}$.

Step8: Solve for 147 (cylinder)

Surface area: Use formula $SA = 2\pi r(r + h)$, with $r = 4$ mm, $h = 13$ mm. $SA=2\pi\times4(4 + 13)=136\pi\approx427.3$ $mm^{2}$. Volume: Use formula $V=\pi r^{2}h$, $V=\pi\times4^{2}\times13=208\pi\approx653.5$ $mm^{3}$.

Answer:

140: Perimeter = 34 cm, Area = 48 $cm^{2}$
141: Circumference $\approx72.3$ mm, Area $\approx415.5$ $mm^{2}$
142: Perimeter = 22 in, Area = 22 $in^{2}$
143: Perimeter $\approx49.7$ m, Area $\approx179.3$ $m^{2}$
144: Surface area = 384 $cm^{2}$, Volume = 512 $cm^{3}$
145: Surface area = 132 $in^{2}$, Volume = 72 $in^{3}$
146: Surface area $\approx439.8$ $cm^{2}$, Volume $\approx461.8$ $cm^{3}$
147: Surface area $\approx427.3$ $mm^{2}$, Volume $\approx653.5$ $mm^{3}$