Question

Which figure below would include pi in the formulas for surface area and volume?

A. Cube

B. Cylinder

C. Pyramid

D. Tetrahedron

Answer 1

(B) cylinder

Explanation:

Since, we know that

(A)Surface area of cube is given as:

`SA=6a^2` and

Volume of cube is given as:

`V=a^3`

Thus, both figures does not includes pi. Hence, this option is incorrect.

(B) Surface area of cylinder is given by:

`SA=2{\pi}rh` and

Volume of cylinder is given as:

`V={\pi}r^2h`

which includes pi, thus this option is correct.

(C) Surface area of pyramid is given as:

`SA=(1)/(3)Perimeter of base{*}height` and

Volume of pyramid is given as:

`V=(1)/(3)area of base{*}height`

And we know that base can be of 2D shapes which do not include pi at all.

Thus, this option is incorrect.

(D) Surface of tetrahedron is given as:

`SA=√(3)a^2` and

Volume of tetrahedron is given as:

`V=(√(2))/(12)a^3`

which does not include pi. Hence, this option is incorrect.

Answer 2

Answer: Option 'b' is correct.

Explanation:

Since we know that

Surface area of cube = 6a²

Volume of cube = a³

So, it does not include pi at all.

Surface area of pyramid is given by

`(1)/(3)`perimeter of base × height

Volume of pyramid is given by

`(1)/(3)`× area of base × height

And we know that base can be of 2D shapes which do not include pi at all.

Surface of tetrahedron is given by

`√(3)a^2`

Volume of tetrahedron is given by

`(√(2))/(12)a^3`

So, it does not include pi.

Surface area of cylinder is given by

`2\pi rh`

Volume of cylinder is given by

`\pi r^2h`

Hence, only cylinder include pi.

Therefore, Option 'b' is correct.