A right trapezoidal prism has base dimensions of $40 c m and 56 c m$ $40 cm and 56 cm$ and a height of $30 c m$ $30 cm$ . Calculate the volume, surface area and the weight of the prism, knowing it is $120 c m$ $120 cm$ high and has a density of $2.5 g \frac{m}{c} m^{3}$ $2.5 gm/cm^3$ ?

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Answer 1 · 2016-11-03T03:59:03

Given

the lengths of two parallel sides of the trapezoidal base of the right prism are

$a = 40 c m and b = 56 c m$ $a=40cm and b=56cm$

And the height of trapezium $c = 30$ $c=30$ cm.

Hence area of trapezoidal base

$A = \frac{1}{2} (a + b) \cdot c$ $A=1/2(a+b)*c$

$= \frac{1}{2} (40 + 56) \cdot 30 c m^{2} = 1440 c m^{2}$ $=1/2(40+56)*30cm^2=1440cm^2$

Height of the prism $h = 120 c m$ $h=120cm$

So volume of the prism

$V = A \times h = 1440 \times 120 = 172800 c m^{3}$ $V=Axxh=1440xx120=172800cm^3$

The density of the prism
$d = 2.5 g c m^{- 3}$ $d=2.5gcm^-3$

So mass of the prism

$M = V \times d = 172800 c m^{3} \times 2.5 g c m^{- 3} = 432000 g = 432 k g$ $M=Vxxd=172800cm^3xx2.5gcm^-3=432000g=432kg$

A right trapezoidal prism has base dimensions of 40cmand56cm40 cm and 56 cm and a height of 30cm30 cm. Calculate the volume, surface area and the weight of the prism, knowing it is 120cm120 cm high and has a density of 2.5gmcm32.5 gm/cm^3?