Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

A square is drawn with the length of the side equal to the diagonal of the cube. if the square area is 72075 cm², then find the side of the cube?

hint Hint:

Area of square=side × side=a²
Diagonal of cube= $square root of 3 cross times side equals square root of 3 a$ unit

The correct answer is: 155 cm.

The length of the square and the diagonal of the cube are coincided. Therefore, the value of the two will be equal.

We are given that,

Area of the square=72,075 cm²
Side of square=Diagonal of cube
Let the edge of the cube be 'a' cm.
As we know,
length of the diagonal of cube= $square root of 3$ ×edge of the cube= $square root of 3$ a cm

The length of the side of the square is equal to the length of the diagonal of the cube.

Area of square(drawn on diagonal of cube)

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals left parenthesis square root of 3 a right parenthesis squared cm squared end cell row cell equals 3 a squared cm squared end cell end table$

We know that, area of square drawn on the diagonal of a cube= 72,075 cm²

Therefore,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 a squared equals 72075 cm squared end cell row cell => a squared equals 72075 over 3 end cell row cell => a squared equals 24025 end cell row cell => a equals square root of 24025 end cell row cell => a equals 155 cm end cell end table$

Therefore , the side of the cube is 155 cm.

Related Questions to study

What are all the possible values of b for which $3 x squared plus b x minus 8$ is it factorable using only integer coefficients and constant?

What are all the possible values of b for which $3 x squared plus b x minus 8$ is it factorable using only integer coefficients and constant?

Find a counterexample to show that the following conjecture is false.
Conjecture: The square of any integer is always greater than the integer.

Find a counterexample to show that the following conjecture is false.
Conjecture: The square of any integer is always greater than the integer.

Three blocks that are in the shape of a cube with each side 3.2 cm are attached end to end. Calculate the T.S.A of the resulting cuboid?

Three blocks that are in the shape of a cube with each side 3.2 cm are attached end to end. Calculate the T.S.A of the resulting cuboid?

parallel

The area of a playground is $36 x squared minus 16 y squared$ . Without removing common factors, factor to possible dimensions of the playground. How are the side-lengths related? What value would you need to subtract from the longer side and add to the shorter side for the playground to be a square?

The area of a playground is $36 x squared minus 16 y squared$ . Without removing common factors, factor to possible dimensions of the playground. How are the side-lengths related? What value would you need to subtract from the longer side and add to the shorter side for the playground to be a square?

What is the first three numbers in the pattern?
−, −, −, 64, 128, 256, …

What is the first three numbers in the pattern?
−, −, −, 64, 128, 256, …

Calculate the maximum number of chocolates of size 2cmx3 cmx5 cm that can be kept in a rectangular box of dimensions 6cmx3cmx15 cm

Calculate the maximum number of chocolates of size 2cmx3 cmx5 cm that can be kept in a rectangular box of dimensions 6cmx3cmx15 cm

parallel

Make and test a conjecture about the sign of the cube of negative integers

Make and test a conjecture about the sign of the cube of negative integers

Given the area of a square, factor it to find the side length.
$text Area end text equals 144 x squared minus 24 x plus 1$

Given the area of a square, factor it to find the side length.
$text Area end text equals 144 x squared minus 24 x plus 1$

Identify the value of c that makes the trinomial factorable using the perfect square pattern.
$x squared plus 16 x plus c$

Identify the value of c that makes the trinomial factorable using the perfect square pattern.
$x squared plus 16 x plus c$

parallel

Given the area of a square, factor it to find the side length.
Area = $36 x squared plus 120 x plus 100$

Given the area of a square, factor it to find the side length.
Area = $36 x squared plus 120 x plus 100$

Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.

Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.

Sum of length, height, and breadth of a rectangular box is 5 √3 cm and the diagonal length is 3√5 cm. Calculate the T.S.A of the rectangular box?

Sum of length, height, and breadth of a rectangular box is 5 √3 cm and the diagonal length is 3√5 cm. Calculate the T.S.A of the rectangular box?

parallel

Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …

Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …

Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …

Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …

Identify the value of c that makes the trinomial factorable using the perfect square pattern.
$2 x squared minus 28 x plus c$

Identify the value of c that makes the trinomial factorable using the perfect square pattern.
$2 x squared minus 28 x plus c$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.