Question

A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.

Answer 1

volume of the prism=100cm3, length=8cm =>area of the base of prism (cross section)=100/8=12.5cm2

Answer 2

The length of a side of the triangle is 5.37 cm.

Step-by-step explanation:

Given : A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle.

To find : The length of a side of the triangle ?

Solution :

The volume of the prism = 100 cm³

The length is 8 cm.

Area of the base of prism (cross section) is given by,

$Area=\frac{Volume}{Length}$

$Area=\frac{100}{8}$

$Area=12.5\ cm^2$

So, area of the equilateral triangle is 12.5 cm².

The area of equilateral triangle formula is $\frac{\sqrt{3}}{4}a^2$

i.e. $12.5=\frac{\sqrt{3}}{4}a^2$

$a^2=\frac{12.5\times 4}{\sqrt3}$

$a^2=28.86$

$a=5.37\ cm$

Therefore, the length of a side of the triangle is 5.37 cm.

#Learn more

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