Question

The perimeter of each face of a cube is 48 cm. Find
(i) It's surface area. (ii) its volume

Answer 1

Answer:

Step-by-step explanation:

If the perimeter of one of the faces of a cube is 40cm, then what is its volume?

Sure career growth with the most awarded university.

William Mccoy

Answered 2 years ago

If the perimeter of one of the faces of a cube is 40cm, then what is its volume?

A cube is a solid that has six faces. Each face is a square which is congruent (has the same size) to the other five faces. Each face or square has four congruent sides, i.e., each side has the same length s; therefore, the formula for the perimeter P of each face is P = 4s. Adjacent faces intersect each other at their intersecting sides of length s to form the edges of the cube for a total of 12 edges, and, consequently, each edge has a length e equal to length s, i.e., e = s; consequently, all 12 edges of a cube are congruent.

P = 4s

40 cm = 4s

(40 cm)/4 = (4s)/4

(40/4) cm = (4/4)s

10 cm = (1)s

10 cm = s

The volume V of a cube is given by the formula V = e³

= (10 cm)³ since e = s = 10 cm.

= (10)(10)(10) cm³

= (100)(10) cm³

= 1,000 cm³ is the volume of the cube in which one of its faces has a perimeter of 40 cm.