Math, asked by sundaskavyanjali299, 6 hours ago

area of total surface of a cube is S square units and length of duagonal is D units, then
a. \: 2d {}^{2}  = s
b. \: d {}^{2}  = s
c. \: 2s {}^{2}  = d
d. \: s { }^{2}  = d

Answers

Answered by Anonymous
51

Relation - Cube

Let me write the complete question for a better understanding. There is something missing in the question.

Complete Question:

Area of total surface of a cube is s square units and length of diagonal is d units, then relation between s and d will be:

a. \: 2d {}^{2} = s

b. \: d {}^{2} = s

c. \: 2s {}^{2} = d

d. \: s { }^{2} = d

We are given that, total surface area of a cube is s square units and length of diagonal is s units. With this information, we are asked to find out the relation between s and d.

Let's consider a units be the edge of side of cube.

We know that, the total surface are of cube is, s = 6a². Therefore,

\implies s = 6 {a}^{2} \\  \\  \implies {a}^{2} =  \frac{s}{6} \\  \\ \implies a =  \sqrt{ \frac{s}{6} }

We know that, the diagonal of cube is, d = √3a. Therefore,

\implies d =  \sqrt{3}a \\  \\ \implies a =  \dfrac{d}{ \sqrt{3}}

The relation between s and d are;

\implies \sqrt{\dfrac{s}{6}} =  \dfrac{d}{ \sqrt{3} }

Now, On squaring both sides, we get:

\implies \bigg( \sqrt{\dfrac{s}{6}}\bigg)^2 = \bigg(\dfrac{d}{ \sqrt{3} }\bigg)^2 \\  \\ \implies  \dfrac{s}{ \cancel{ \: 6 \: }} =  \dfrac{ {d}^{2} }{ \cancel{ \: 3 \: }} \\  \\  \implies \dfrac{s}{2} = {d}^{2}\\  \\ \implies \boxed{\bf{s = 2 {d}^{2}}}

Hence, the relation between s and d is s = 2 {d}^{2}. So, option (a) 2d^{2} = s is correct.

\rule{90mm}{2pt}

MORE TO KNOW

  • C.S.A of cube = 4a²
  • T.S.A of cube = 6a²
  • Volume of cube = a³
  • Diagonal of cube = √3a
  • Volume of cylinder = πr²h
  • T.S.A of cylinder = 2πrh + 2πr²
  • Volume of cone = ⅓ πr²h
  • C.S.A of cone = πrl
  • T.S.A of cone = πrl + πr²
  • Volume of cuboid = l × b × h
  • C.S.A of cuboid = 2(l + b)h
  • T.S.A of cuboid = 2(lb + bh + lh)
  • Volume of sphere = 4/3πr³
  • Surface area of sphere = 4πr²
  • Volume of hemisphere = ⅔ πr³
  • C.S.A of hemisphere = 2πr²
  • T.S.A of hemisphere = 3πr²
Answered by Anonymous
40

Answer:

Solutions :-

 \large \dagFirst let understand your question .

In the question given that area of total surface of a cube is S square units an d length of diagonal is D units .Then,

  1. 2d^2=S
  2. d^2=S
  3. 2S^2 = d
  4. s^2 = s

Here in Th is question we should need to find relation between S and d.

So,

We know that,total surface area of cube that is ,

  • S = 6a^2.

  • a^2= S/6

  • a = root of S/6.

And also we know That,

  • Diagonal of cube =root 3 a

  • d = root 3 × a

  • a=d/root3

And Then,

  • The relation between S And s is:

  • root s/6 = d/root 3

Then ,

  • By taking square root on both of the sides we get,

  • s/6 = d^2/3

  • s/2= d^2

  • s= 2d^2.

Therefore,

  • Option A is the perfect answer to your Question.

Thank you .

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