Question

Calculate the following related to square based prisms:
(a) Volume if the base is $3$cm and height is $6$cm;
(b) Volume if area of base is $20m^2$ and height is $4.5$m;
(c) Height if the volume is $490c{m}^3$ and edge of the base is $7$cm;
(d) Base if volume is $968c{m}^3$ and height is $8$cm.

Answer 1

(a) The area of the base $B=s^2$ with $s=3$ cm is:

$B=s^2=3^2=9$ cm${}^2$

The general formula for volume of prism is $V=Bh$ where $B$ is the area of the base and $h$ is the height.

Since area of the base is $B=9$ cm${}^2$ and the height $h=6$ cm, therefore, the volume is:

$V=Bh=9\times 6=54$ cm${}^3$

Hence, the volume of the prism is $54$ cm${}^3$.

(b) The general formula for volume of prism is $V=Bh$ where $B$ is the area of the base and $h$ is the height.

Since area of the base is $B=20$ m${}^2$ and the height $h=4.5$ m, therefore, the volume is:

$V=Bh=20\times 4.5=90$ m${}^3$

Hence, the volume of the prism is $90$ m${}^3$.

(c) The area of the base $B=s^2$ with $s=7$ cm is:

$B=s^2=7^2=49$ cm${}^2$

The general formula for volume of prism is $V=Bh$ where $B$ is the area of the base and $h$ is the height.

Since area of the base is $B=49$ cm${}^2$ and the volume is $V=490$cm${}^3$, therefore, the height is:

$V=Bh\Rightarrow 490=49h\Rightarrow h=\frac{490}{49}=10$

Hence, the height of the prism is $10$ cm.

(d) The general formula for volume of prism is $V=Bh$ where $B=s^2$ is the area of the base and $h$ is the height.

Since height is $h=8$ cm and the volume is $V=968$cm${}^3$, therefore, the base is:

$V=s^{2}h\Rightarrow 968=8s^2\Rightarrow s^2=\frac{968}{8}=121\Rightarrow s=\sqrt{121}=11$

Hence, the base of the prism is $11$ cm.