Question

part 2: applying (4 points)directions: solve the following problems by finding the volume and surface area.you must show work to get full credit.1. surface area ____ $yd^{2}$volume = __ $yd^{3}$2.surface area __ $cm^{2}$volume = ____ $cm^{3}$

Explanation:

Problem 1 (Cylinder):

Step1: Recall surface area formula

Surface area of a cylinder: $SA = 2\pi r^2 + 2\pi r h$
Given $r=3$ yd, $h=10$ yd

Step2: Calculate surface area

$$\begin{align} SA &= 2\pi(3)^2 + 2\pi(3)(10) \\ &= 2\pi(9) + 60\pi \\ &= 18\pi + 60\pi \\ &= 78\pi \approx 244.92 \end{align}$$

Step3: Recall volume formula

Volume of a cylinder: $V = \pi r^2 h$

Step4: Calculate volume

$$\begin{align} V &= \pi(3)^2(10) \\ &= \pi(9)(10) \\ &= 90\pi \approx 282.74 \end{align}$$

Problem 2 (Rectangular Prism):

Step1: Recall surface area formula

Surface area of a prism: $SA = 2(lw + lh + wh)$
Given $l=10$ cm, $w=8$ cm, $h=3$ cm

Step2: Calculate surface area

$$\begin{align} SA &= 2((10)(8) + (10)(3) + (8)(3)) \\ &= 2(80 + 30 + 24) \\ &= 2(134) \\ &= 268 \end{align}$$

Step3: Recall volume formula

Volume of a prism: $V = lwh$

Step4: Calculate volume

$$\begin{align} V &= (10)(8)(3) \\ &= 240 \end{align}$$

Answer:

1. Surface area: $78\pi$ or $244.92$ yd², Volume: $90\pi$ or $282.74$ yd³
2. Surface area: $268$ cm², Volume: $240$ cm³