Question

A triangular prism has a volume of 5 m3. If each dimension of the prism is tripled, what is the new volume of the prism?
Answer
135 m3
45 m3
15 m3
405 m3

Answer 1

i got 45 m3

Answer 2

Volume of a triangular prism= Area of the base \(\times\) height
\[V=\sqrt {3} \frac{a^2}{2} \times h\]
a= edge of the base triangle
h= height of prism
\[5=\sqrt {3} \frac{a^2}{2} \times h\]
Now each dimension is tripled
new edge= 3a
new height=3h
so
\[V=\sqrt {3} \frac{(3a)^2}{2} \times 3h\]
we get
\[V=9 \times 3 \sqrt {3} \frac{(a)^2}{2} \times h\]
\[V=27 \times \sqrt {3} \frac{(a)^2}{2} \times h\]
We know
\[5=\sqrt {3} \frac{a^2}{2} \times h\]
so
\[V=27*5=135 m^3\]

Answer 3

tysm!