area of total surface of a cube is S square units and length of duagonal is D units, then
![a. \: 2d {}^{2} = s a. \: 2d {}^{2} = s](https://tex.z-dn.net/?f=a.+%5C%3A+2d+%7B%7D%5E%7B2%7D++%3D+s)
![b. \: d {}^{2} = s b. \: d {}^{2} = s](https://tex.z-dn.net/?f=b.+%5C%3A+d+%7B%7D%5E%7B2%7D++%3D+s)
![c. \: 2s {}^{2} = d c. \: 2s {}^{2} = d](https://tex.z-dn.net/?f=c.+%5C%3A+2s+%7B%7D%5E%7B2%7D++%3D+d)
![d. \: s { }^{2} = d d. \: s { }^{2} = d](https://tex.z-dn.net/?f=d.+%5C%3A+s+%7B+%7D%5E%7B2%7D++%3D+d)
Answers
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:
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 units be the edge of side of cube.
We know that, the total surface are of cube is, s = 6a². Therefore,
We know that, the diagonal of cube is, d = √3a. Therefore,
The relation between and
are;
Now, On squaring both sides, we get:
Hence, the relation between and
is
. So, option (a)
is correct.
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
Answer:
Solutions :-
First 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,
- 2d^2=S
- d^2=S
- 2S^2 = d
- 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.