Question

the figure below shows a shed in the shape of a rectangular prism. note that the shed has a floor.
(a) use the calculator to find the surface area and volume of the shed. make sure to include the correct units.
surface area:
volume:
(b) the shed is used for storage. which measure would be used to find how much the shed holds?
○ surface area ○ volume
(c) the shed is painted yellow. which measure helped the shed maker know how much paint to buy?
○ surface area ○ volume

Explanation:

Step1: Calcular el área de superficie

La fórmula para el área de superficie de un prisma rectangular es \( SA = 2(lw + lh + wh) \), donde \( l = 15 \) ft, \( w = 8 \) ft, \( h = 9 \) ft.
Sustituimos los valores: \( SA = 2((15\times8) + (15\times9) + (8\times9)) = 2(120 + 135 + 72) = 2(327) = 654 \) \( ft^2 \).

Step2: Calcular el volumen

La fórmula para el volumen de un prisma rectangular es \( V = l\times w\times h \).
Sustituimos los valores: \( V = 15\times8\times9 = 1080 \) \( ft^3 \).

Step3: Resolver (b)

Para saber cuánto contiene el cobertizo (almacenamiento), usamos el volumen, ya que el volumen mide el espacio interior.

Step4: Resolver (c)

Para saber cuánta pintura se necesita, usamos el área de superficie, ya que la pintura se aplica en la superficie externa.

Answer:

(a) Área de superficie: \( 654 \) \( ft^2 \), Volumen: \( 1080 \) \( ft^3 \)
(b) Volumen
(c) Área de superficie