Question

the figure below shows a juice box in the shape of a rectangular prism.
(a) use the calculator to find the volume and surface area of the box.
make sure to include the correct units.
volume:
surface area:
(b) the juice box is coated with wax.
which measure helped the manufacturer know how much wax to buy?
○ volume ○ surface area
(c) the juice box is to be filled with juice.
which measure would be used to find the amount of juice the box will hold?
○ volume ○ surface area

Explanation:

Step1: Calcular el volumen

La fórmula para el volumen de un prisma rectangular es \( V = l \times w \times h \), donde \( l = 11 \, \text{cm} \), \( w = 7 \, \text{cm} \) y \( h = 10 \, \text{cm} \).
\( V = 11 \times 7 \times 10 = 770 \, \text{cm}^3 \)

Step2: Calcular el área de superficie

La fórmula para el área de superficie de un prisma rectangular es \( SA = 2(lw + lh + wh) \).
Sustituyendo los valores: \( lw = 11 \times 7 = 77 \), \( lh = 11 \times 10 = 110 \), \( wh = 7 \times 10 = 70 \).
\( SA = 2(77 + 110 + 70) = 2(257) = 514 \, \text{cm}^2 \)

(b) Explicación para la cera

La cera cubre la superficie exterior, así que se usa el área de superficie.

(c) Explicación para el jugo

El jugo llena el interior, así que se usa el volumen.

Answer:

(a) Volumen: \( 770 \, \text{cm}^3 \), Área de superficie: \( 514 \, \text{cm}^2 \)
(b) Surface area
(c) Volume