// //]]>
##### Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Next time you have a doubt while studying, you know where to go. By simply posting your questions on Question & Answer Forum, you can have them answered by academic experts. You can also find related videos and explanations for better understanding.

Find the length of the longest rod that can be placed in a room

Given length l = 12 m
breadth b = 9 m and height h = 8 m
Longest rod that can be placed in a room is nothing but its diagonal.
Length of diagonal of a cuboid = √...

Oct 11

• 1 Like
• 65456 Views

Oct 11

A cone ,hemisphere and a cylinder stand on equal base

Volume of cone = (1/3)πr 2h
Volume of hemisphere = (2/3) πr 3
Volume of cylinder =  πr 2 h
Given that cone, hemisphere and cylinder have equal base a...

Jan 9

• 5 Likes
• 61664 Views

Jan 9

A semi circular sheet of metal of diameter 28 cm

Given diameter = 28 cm
Circumference of semi circle = πr
= (22/7) x 14 = 44 cm
This becomes circumference of base of cone
2 πR =...

Feb 27

• 5 Likes
• 52529 Views

Feb 27

Raghunath answered 4 year(s) , 3 month(s) ago

A sphere and a cube have the same surface area . show that the ratio of the volumes of the sphere to that of the cube is √6 : √π

Let r and a be the radius of the sphere and edge of the cube respectively.

Given, Surface area of sphere = Surface area of cube

4πr2 = 6a2

(r/a

...

Mar 9

• 4 Likes
• 50590 Views

Mar 9

The outer dimensions of a closed wooden box are 10 cm x 8 cm x 7 cm.

Given outer length = 10 cm
Outer height = 7 cm
Outer volume = length × breadth × height
= 10 × 8 × 7 = 560 cm3
Thickness of wood

...

Oct 16

• 3 Likes
• 41767 Views

Oct 16

Raghunath answered 4 year(s) , 4 month(s) ago

Three cubes each of side 5 cm are joined to the end. find the surface area of the resultant cuboid.

Sol:

Given, each side of the cube is 5 cm.

When three cubes are joined end to end, then the resulting solid is a cuboid.

Length of the cuboid, l = 2 × each side of the cube = 2 × 5

...

Feb 4

• 2 Likes
• 38237 Views

Feb 4

Raghunath answered 5 year(s) , 1 month(s) ago

AB and CD are 2 parallel chords of a circle such that AB=10cm CD =24cm if 2 chords are on the opp side of the centre and the distance bw them is 17cm find the radius of

Sol :

Given AB and CD are two chords of a circles D and E are midpoints of AB ,CD respectively.
CD = DB = 12 cm and AE = EB = 5 cm
Distance between two chords = 17 cm
Di...

Mar 1

• 2 Likes
• 32669 Views

Mar 1

Ramesh answered 4 year(s) , 3 month(s) ago

The length of longest pole that can be put in a room of dimensions (10m x 10m x 5m) is _________.

Length of the longest pole that can be put in a room = Length of the diagonal inside the room

Length of the diagonal =  √( l 2   + b 2...

Mar 9

• 6 Likes
• 31033 Views

Mar 9

daniel answered 1 year(s) , 3 month(s) ago

Write all the formulas in Surface areas and volumes.

Sol:
If l, b and h are length, breadth and height of a cuboid, then
•  lateral surface area = 2h (l + b)
•  total surface area of the cuboid = 2(lb + bh + lh)
...

Nov 29

• 3 Likes
• 30971 Views

Nov 29

Raghunath answered 4 year(s) , 3 month(s) ago

A sphere ,cylinder and a cone of same radius and same height find the ratio of their CSA

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.

Then
Curved surface area of Sphere= 4πr²

Curved surface area of cylinder = 2πr(2r) = 4πr²

...

Feb 24

• 2 Likes
• 29208 Views

Feb 24

Agam answered 1 year(s) , 9 month(s) ago

A well with inside diameter of 10m is dug 14m deep

Given radius of the well = 5 m
Height of the well = 14 m
Width of the embankment = 5 m
Therefore radius of the embankment = 5 + 5 = 10 m
Let h be the height of the embankment...

Mar 13

• 1 Like
• 27042 Views

Mar 13

How many meters of cloth 5m wide will be required to make a conical tent,the radius of whose base is 7m and whose height is 24m?

Given, r = 7 m

h = 24 m

∴ slant height l = √(r2 + h2) = √(49 + 576) = √625 = 25 m

CSA of the cone = πrll = 22/7 x 7 x 25 = 550 m2

Area of the

...

Mar 3

• 2 Likes
• 24636 Views

Mar 3

Agam answered 1 year(s) , 7 month(s) ago

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m

Internal radius, r = 30 cm
Thickness, w = 5 cm
External radius, R = 30 + 5 = 35 cm
Here volume of cuboid = volume of hollow cylinder
440 × 260 ×100 = π(R 2 – r 2) h
⇒...

Oct 19

• 0 Like
• 23191 Views

Oct 19

Raghunath answered 4 year(s) , 5 month(s) ago

The surface areas of two spheres are in the ratio 1:4.find the ratio of their volumes.

Sol:
Given that surface areas of two spheres are in the ratio 1:4.

4πr² : 4πR²  = 1 : 4

r : R = 1 : 2.

Now ratio of volumes of two spheres  =  (4/3)πr3 : (4/3)πR

...

Dec 21

• 1 Like
• 21613 Views

Dec 21

Kishore answered 5 year(s) , 8 month(s) ago

A cylinder of radius 12cm contains water to a depth of 20cm.

Given radius of the cylinder, r = 12 cm
It is also given that a spherical iron ball is dropped into the cylinder and the water level raised by 6.75 cm
Hence volume of water displaced = volume of...

Oct 16

• 3 Likes
• 20282 Views

Oct 16

Kishore answered 5 year(s) , 6 month(s) ago

The diameter of a sphere is decreased by 25%

Curved surface area of the sphere = 4πr 2

Given diameter is decreased by 25%
Hence the new diameter=

Nov 23

• 0 Like
• 18500 Views

Nov 23

Raghunath answered 4 year(s) , 6 month(s) ago

Find the outer and inner radii of the pipe.

Sol:

Let r and R be the inner and outer radius of the cylindrical metallic pipe respectively.

h be the height of the metallic pipe = 14 cm

Difference between the Curved surface a

...

Nov 22

• 1 Like
• 17676 Views

Nov 22

Kishore answered 5 year(s) , 5 month(s) ago

if v is volume of cubiod of dimensions a,b,c

Given dimensions of cuboid are a, b and c.
Therefore, volume of cuboid, V = abc  → (1)
Surface area of cuboid, S = 2(ab + bc + ca)   → (2)
Now divide (2) with (1), we get
...

Jan 4

• 5 Likes
• 17509 Views

Jan 4

Kishore answered 5 year(s) , 2 month(s) ago

A right angled triangle ABC with sides 5cm, 12cm, 13cm is revolved

Given a right angle triangle with sides 5cm, 12 cm and 13 cm
Hence hypotenuse is 13 cm
Given that the triangle is revolved about 12 cm side
Therefore, radius r = 5 cm and height  h = 12...

Mar 5

• 0 Like
• 16565 Views

Mar 5

Kishore answered 5 year(s) , 8 month(s) ago

The diagonal of cube is √12 cm . What is its edge?

Given length of diagonal of a cube = √12 cm
Recall that length of diagonal of a cube = √3 × Length of edge of the cube
⇒ √12 = √3 × Length of edge of the cube
∴  Length of edge of the cu...

Oct 11

• 3 Likes
• 16082 Views

Oct 11

###### Like NextGurukul? Also explore our advanced self-learning solution LearnNext
Offered for classes 6-12, LearnNext is a popular self-learning solution for students who strive for excellence
Explore
Animated Video
lessons
All India
Test Series
Interactive Video
Experiments
Best-in class
books