Question

How many cubic blocks with a side length of 3/8 cm will be required

to find the volume of a cube with a side length of 3/4 cm?

A.
8
B.
10
C.
12
D.
14
E.
16

Answer 1

The correct answer is option A.

8 blocks are needed to fill the box.

Explanation:

Given data:

Side length of a block = 3/8 cm

Side length of main block = 3/4 cm

How many blocks are needed to fit in main blocks = ?

Solution:

Volume = length³

Volume of one simple block = (3/8)³ = 27/512 cm³

Volume of one Main block = (3/4)³ = 27/64 cm³

Blocks are needed to fit in main blocks = (27/64) ÷ (27/512) = 8

Answer = 8 blocks

Hence 8 simple small blocks of one side length 3/8 cm will needed to fit in the main block of side length 3/4 cm.

Answer 2

The correct answer is A.

EXPLANATION

The volume of a cube is given by

`V=l^3`

First we find the volume of the cube with side length
`(3)/(4)cm`

`V_(Cube)=((3)/(4))^3`

`V_(Cube)=(27)/(64) cm^3`

Next, we find the volume of the cubic block with side length
`(3)/(8)cm`

`V_(Block)=((3)/(8))^3`

`V_(Block)=(27)/(512) cm^3`

We divide the volume of the cube by the volume of the block to get the number of cubic blocks

`Number\: of \: blocks=\frac{(27)/(64)} {(27)/(512)}`

`Number\: of \: blocks=(27)/(64) * (512)/(27)`

`Number\: of \: blocks=(1)/(1) * (8)/(1)=8`