A right trapezoidal prism has base dimensions of #40 cm and 56 cm# and a height of #30 cm#. Calculate the volume, surface area and the weight of the prism, knowing it is #120 cm# high and has a density of #2.5 gm/cm^3#?

Question

James Atkins · Accepted Answer

Given the lengths of two parallel sides of the trapezoidal base of the right prism are #a=40cm and b=56cm# And the height of trapezium #c=30#cm. Hence area of trapezoidal base #A=1/2(a+b)*c# #=1/2(40+56)*30cm^2=1440cm^2# Height of the prism #h=120cm# So volume of the prism #V=Axxh=1440xx120=172800cm^3# The density of the prism
#d=2.5gcm^-3# So mass of the prism #M=Vxxd=172800cm^3xx2.5gcm^-3=432000g=432kg#

Evelyn Arboleda · Answer

undefined Volume: $ V = \text{Base area} \times \text{Height} $

Surface Area: $ SA = 2(\text{Base area}) + \text{Lateral area} $

Weight: $ W = \text{Volume} \times \text{Density} $

Given:
Base dimensions: 40 cm and 56 cm
Height: 30 cm
Total height: 120 cm
Density: 2.5 g/cm³

Volume:
$$ V = (40 \times 56) \times 30 $$

Surface Area:
$$ SA = 2(40 \times 56) + (40 + 56) \times 120 $$

Weight:
$$ W = V \times \text{Density} $$

Plug in the values to calculate each:

Volume: $ V = 67200 \, \text{cm}^2 $

Surface Area: $ SA = 2(2240) + 21600 $

Weight: $ W = 67200 \times 2.5 $

After calculating:

Volume: $ V = 2016000 \, \text{cm}^3 $

Surface Area: $ SA = 107200 \, \text{cm}^2 $

Weight: $ W = 5040000 \, \text{g} $

Converting weight to kilograms: $ W = 5040 \, \text{kg} $