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

Answer:

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=LengthVolume

Area=\frac{100}{8}Area=8100

Area=12.5\ cm^2Area=12.5 cm2

So, area of the equilateral triangle is 12.5 cm².

The area of equilateral triangle formula is \frac{\sqrt{3}}{4}a^243a2

i.e. 12.5=\frac{\sqrt{3}}{4}a^212.5=43a2

a^2=\frac{12.5\times 4}{\sqrt3}a2=312.5×4

a^2=28.86a2=28.86

a=5.37\ cma=5.37 cm

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

#Learn more

A rectangular prism has a volume of V= 2x^3+6x^2+4x. What could the dimensions of this prism be?

Step-by-step explanation:

I hope this helps.