Question

6. A prism has bases that are equilateral triangles with sides lengths of 10 inches and a length of 30 inches.
Determine the volume of the prism to the nearest cubic inch. Show how you arrived at your answer
30 in
10 in
ON​

Answer 1

Answer:

The volume of the prism is $1,299\ in^{3}$

Step-by-step explanation:

we know that

The volume of the prism is equal to

$V=BL$

where

B is the area of the triangular base

L is the length of the prism

we have

$L=30\ in$

Find the area of the base B

The area of a equilateral triangle is equal to

$B=\frac{1}{2}(10)^{2} sin(60\°)$

$B=25\sqrt{3}\ in^{2}$

substitute

$V=(25\sqrt{3})(30)=1,299\ in^{3}$

Answer 2

The volume of the traingular prism is 1,280.85 in³.

Volume of the prism

The volume of the prism is determined using the following formulas as show below;

V = Bh

where;

• B is the base area of the prism
• h is the height of the prism

Base area is calculated as follows;

$A = \frac{a^2\sqrt{3} }{4} \\\\A = \frac{10^2 \times \sqrt{3} }{4} \\\\A = 25\sqrt{3} \ in^2$

Height of the prism

$L^2 = (\frac{a}{2} )^2 + h^2\\\\h^2 = L^2 - (\frac{a}{2} )^2\\\\h^2 = 30^2 - (\frac{10}{2} )^2\\\\h^2 = 875\\\\h = \sqrt{875} \\\\h = 29.58 \ in$

Volume of the prism

V = 25√3 x 29.58

V = 1,280.85 in³

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