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

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

• Dividing both sides of equation by 2      
•  

• Dividing both sides of equation by 26

Therefore,
The dimensions of cuboid are,
Length = 4x = 4(5)= 20
Breadth= 3x = 3(5) =15
Height = 2x=2(5)= 10
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

Hint:- Volume of a cone = ()πr²h
Solution :- We have given the dimensions of a cone
Diameter = 12 cm
Radius, r = = 6 cm
Height, h = 8 cm
We have to find the volume of the given cone
We know that
Volume of a cone = ()πr²h
= ()(3.14)(6 x 6) (8)
= ()(3.14) (36 x 8)
= ()(3.14)(288)
= 904.
= 301.4 cm³
Therefore correct option is c) 301.4 cm³.

Ans:- Option B
Given, 
Divide -2ab into -ab and -ab so that (-ab)(-ab) =   we get 
Taking common elements we get  
Taking (a-b) common gives 
∴ Option B is correct

• Step 1:We have given the total surface area of the cube.

Area = 346.56 cm²

• Step 2: We know that

Surface Area = 6a²
                                                                               346.56 = 6a²

• ^·          Step 3: For finding the side firstly divide both sides if equation by 6

• Step 4:- Taking square root of both sides we get,

• ^·          Step 5: Therefore, the length of side of the given cube is 7.6 cm².
  • Therefore, the correct answer is option B) 7.6 cm.

Hint:- Volume of a cone = ()πr²h
Solution :- We have given the dimensions of a cone
Radius, r = 4 in
Height, h = 4 in
We have to find the volume of the given cone
We know that
Volume of a cone = ()πr²h
= ()(3.14)(4 x 4) (4)
= ()(3.14) (16 x 4)
= ()(3.14)(64)
= 200.
= 66.9 in³
Therefore correct option is b) 66.9 in³.

• We are given the dimensions of cuboid.

length = 40cm = l
breadth = 20cm = b
height = 10cm = h

• We will calculate the LSA of given cuboid

We know that,
The Lateral Surface area of cuboid = 2h( l + b)

• By using the above formula of the lateral surface area of the cuboid, we get

The lateral surface area of the given cuboid is,

= 2h( l + b)

= 2  10  (40 + 20)

= 20  (60)

LSA= 1200 cm²
Therefore the Lateral surface area of the given cuboid is 1200 cm².
The correct answer is option d) 1200.

Hint:- Volume of frustum of cone = 
Solution:- We have given the dimensions of a bucket which is of frustrum shape
Top diameter = 42 cm
Top radius, R = 21 cm
Bottom diameter = 14
Bottom radius, r = 7 cm
Height of frustrum , h = 24 cm
Therefore capacity of bucket = volume of bucket


= 
= 
= 
= 176 × 91
= 
Therefore, the correct option is a)16016 cm³

• We have given,

LSA of cuboid = 900cm²
Breadth= 10 cm
Length = 20 cm

• We know that ,

LSA of cuboid = 2h( l + b)

• Insert the values in the above equation.

900 = 2h (20 + 10)
900 = 2h(30)
Divide both sides of equation by 30, we get

Divide both sides of equation by 2, we get
h = 15

• Therefore the height of given cuboid is 15 cm.
• The correct option is option a) 15 .

HINT :- using the formula  factorize the given expression
Ans:-  is the factorized form of the given expression.
Explanation :-
Given, 
Taking out common factor -3x out of equation , we get 
Write
Applying
Here a = x ; b = 3
We get , 
∴  is the factorized form of the given expression.

Hint:- Volume of a cone = ()πr²h
Solution :- We have given the dimensions of a cone
Radius , r = 6 m
Volume of cone = 84π m³
We have to find the height of the given cone
Let height of the cone be h
We know that
Volume of a cone = ()πr²h
84π = () π (6 x 6) (h)
Divide both sides of equation by π
84 = (2 x 6) (h)
84 = 12h)
h =
h = 7 m
Therefore correct option is a) 7m

HINT :- using the formula   factorize the given expression
Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.
Explanation :-
Given,
Taking out common factor 2 out of equation , we get 
Write 
Applying  
We get , 
∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

Hint:- Slant height L = 
where h is height
r is radius of base of cone

Solution:- We have given the dimensions of a right circular cone
Base diameter = 14 cm
Radius, r = = 7 cm
Height, h = 24 cm
Let us find the slant height
L = 
L = 
= 
= 
L = 25 cm
Therefore, the correct option is d) 25 cm.

HINT :- using the formula  factorize the given expression
Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.
Explanation :-
Given, 
Taking out common factor 16 out of equation , we get 
Write
Applying 
Here a = 2xy ; b = 3z
We get , 
∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

• Step 1:We have given area of one face of the cube.

Area of face = 81

• Step 2: For total surface area, find out the product of the square of side length by 6.

Surface area =  6 (area of face)
                      =  6 (81)
                      =   486

• Step 4: Therefore, the surface of the given cube is 486.
• Therefore, the correct answer is option A) 486 .