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 total surface area of a cube is 846 cm². Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

15 cm, 12 cm and 9 cm
12 cm , 9 cm and 18 cm
15 cm , 24 cm ,9 cm
9 cm , 24 cm ,15 cm

hint Hint:

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
Where,
l = length
b = breadth
h = height

The correct answer is: 15 cm, 12 cm and 9 cm

We have given the surface area of cube = 846cm²
And the ratio of height breadth and length is 3:4:5
Let , height = 3x,
Breadth =4x,
Length = 5x
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
$2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846$

$2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846$
2(47x²) = 846
Divide both sides by 2,
$table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table$
Divide both sides by 47,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 423 over 47 end cell row cell x squared equals 9 end cell end table$
Taking square root
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals square root of 9 end cell row cell x equals 3 end cell end table$
The dimensions of cuboid are,
Height = 3x=3(3)= 9
Breadth= 4x =4(3) =12
Length = 5x = 5(3)= 15
Therefore the option a)15cm , 12cm , 9cm is correct.

Related Questions to study

A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

parallel

Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
Use 3.14 for pi.

Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
Use 3.14 for pi.

Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

parallel

The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

parallel

Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

Surface area of a cube is 443.76 cm² . Find the volume of it?

Surface area of a cube is 443.76 cm² . Find the volume of it?

Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

parallel

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?

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?

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

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

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

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.