Question

Each side of a cube is measured to be 5.402 cm. Find the total surface area and the volume of the cube in appropriate significant figures.

Please answer correctly to get brainliest and 30 points, or i will report you!​

Answer 1

Given:

Length of side of cube,a = 5.402 cm

To Find:

The total surface area and the volume of the cube in appropriate significant figures

Solution:

We know that,

• In multiplication, number of significant figures of product is determined by the number having lowest significant figures  
• For a cube

$\pink{\boxed{\bf{Total\:Surface\:Area=6a^{2}}}}$

$\pink{\boxed{\bf{Volume=a^{3}}}}$

where

a is length of side of cube

$\rule{190}{1}$

Let the total surface area of given cube be 'T' and volume of given cube be 'V'.

So,

$\longrightarrow\rm{T=6a^{2}}$

$\longrightarrow\rm{T=6\times(5.402)^{2}}$

$\longrightarrow\rm{T=6\times29.181604}$

$\longrightarrow\rm{T=175.089624}$

On rounding off to appropriate significant figures, we get

$\longrightarrow\rm{T=175.1\:cm^{2}}$

Also,

$\longrightarrow\rm{V=a^{3}}$

$\longrightarrow\rm{V=(5.402)^{3}}$

$\longrightarrow\rm{V=157.639024808}$

On rounding off to appropriate significant figures, we get

$\longrightarrow\rm{V=157.6\:cm^{3}}$

Hence, the total surface area and the volume of the cube in appropriate significant figures is 175.1 cm² and 157.6 cm³ respectively.

Answer 2

GIVEN :-

Length of each side of a cube = 5.402 cm

TO FIND :-

• The total surface area(TSA) of the cube.

• The volume of the cube.

FORMULAE TO BE USED :-

• TSA of a cube = 6 × (side)²

• Volume of a cube = (side)³

SOLUTION :-

Given, side = 5.402 cm.

$\sf{TSA=6\times(5.402)^2}\\\\\sf{\longrightarrow TSA=6\times 29.181604}\\\\\sf{\longrightarrow TSA=175.089624\ cm^2}$

Taking an approximate value, we get :-

TSA = 175.1 cm²

$\rule{200}{2}$

Now,

$\sf{Volume=(side)^3}\\\\\sf{\longrightarrow Volume=(5.402)^3}\\\\\sf{\longrightarrow Volume=157.639024808\ cm^3}$

Taking an approximate value, we get :-

Volume = 157.6 cm³

$\rule{200}{2}$

Therefore, the total surface area of the cube is 175.1 cm² and the volume of the cube is 157.6 cm³.