Question

6.
A rectangular block of cheese is 0.24 m long,
0.19 m wide and 0.15 m high.
(a) If the block of cheese is moulded to form a
cube, find the length of each side of the cube.
(b) Find the number of 2-cm cubes of cheese that
can be cut from the rectangular block.​

Answer 1

Answer:

Step-by-step explanation:

(A)

0.24 × 0.19 × 0.15 = 0.00684

∛0.00684 = 0.189824399

round off to 3 s.f., 0.190

Answer 2

Answer:

(a) Length of the side of cube = 18.98cm

(b) The number of 2cm cubes that can be cut = 855

Step-by-step explanation:

Given,

The length of cheese block= 0.24m = 24cm

breadth of cheese block = 0.19m = 19cm

Height of the cheese block = 0.15m = 15cm

Recall the formulas

The volume of the cuboid = length×breadth ×height

The volume of the cube = a³, where 'a' is the length of the side of the cube

(a) To find,

The length of the side of a cube, if the cheese cube is molded into a cube

Since the  cheese blockis moldedd to form a cube, then we have

The volume of the cheese block = Volume of cube

The volume of cheese block = Volume of the cuboid

=  24× 19 ×15

= 6840cm³

Since the volume of the cheese block = Volume of the cube, we have

Volume of the cube = 6840cm³

a³ = 6840

$a = \sqrt[3]{6840}$ = 18.98cm

Length of a side of cube = 18.98cm

(b)  To find,

The number of 2cm cubes of cheese can be cut from the cheese block.

Let 'n' be the number of 2cm cubes that can be cut

Then we have,

The volume of the cheese block = n× Volume of 2cm cube

6840 = n×2³

6840 = x×8

n = $\frac{6840}{8}$ = 855

The number of 2cm cubes that can be made = 855

(a) Length of the side of cube = 18.98cm

(b) The number of 2cm cubes that can be cut = 855

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