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

The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm². Find its length, breadth, and height respectively?

10 cm , 15 cm, 20 cm
15 cm , 10 cm ,20 cm
15 cm , 20 cm , 10 cm
20 cm,15cm , 10 cm

hint Hint:

We have given three different dimensions of rectangular box (cuboid) ,
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where
l → length of the cuboid
b → breadth of the cuboid
h → height of the cuboid

The correct answer is: 20 cm,15cm , 10 cm

Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².
We have to find Length, breadth & height of cuboid.

Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀

Now, As we know that, total surface area of cuboid is given by,

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where, l, b & h are length, breadth and height of cuboid respectively.

We have , length = 4x

Breadth, b = 3x
Height, h = 2x
TSA = 1300 cm²

Putting the values in the formula

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 left square bracket left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 3 x right parenthesis left parenthesis 2 x right parenthesis plus left parenthesis 2 x right parenthesis left parenthesis 4 x right parenthesis right square bracket equals 1300 end cell row cell 2 open square brackets 12 x squared plus 6 x squared plus 8 x squared close square brackets equals 1300 end cell row cell 2 open parentheses 26 x squared close parentheses equals 1300 end cell end table$

Dividing both sides of equation by 2

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 26 x squared equals 1300 over 2 end cell row cell 26 x squared equals 650 end cell end table$

Dividing both sides of equation by 26

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 650 over 26 end cell row cell x squared equals 25 end cell row cell x equals square root of 25 end cell row cell x equals 5 end cell end table$
Therefore,
The dimensions of cuboid are,
Length = 4x = 4(5)= 20
Breadth= 3x = 3(5) =15
Height = 2x=2(5)= 10
$therefore$ Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.
Therefore the correct option is d) 20 cm,15cm , 10 cm

Related Questions to study

Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

$a squared minus 2 a b plus b squared equals$

$a squared minus 2 a b plus b squared equals$

Find out the side of cube if the complete surface area is given to be 346.56 cm².

Find out the side of cube if the complete surface area is given to be 346.56 cm².

parallel

Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm
respectively .Find the capacity of the bucket

The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm
respectively .Find the capacity of the bucket

parallel

Given LSA of a cuboid is 900cm²and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

Given LSA of a cuboid is 900cm²and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

Factor the given expression completely.
$negative 3 x cubed plus 18 x squared minus 27 x$

Factor the given expression completely.
$negative 3 x cubed plus 18 x squared minus 27 x$

Find the height of a cuboid whose base area is 180cm² and volume is 900cm²

Find the height of a cuboid whose base area is 180cm² and volume is 900cm²

parallel

A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

What is the factored form of $50 x squared minus 32 y squared$ ?

What is the factored form of $50 x squared minus 32 y squared$ ?

Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

parallel

Factor the given expression completely.
$64 x squared y squared minus 144 z squared$

Factor the given expression completely.
$64 x squared y squared minus 144 z squared$

Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A

Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A

A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel

A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel

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.