Question

1. The total surface area of a cube 1176cm?. Find its volume.
2. The curved surface area of a cylinder is 4400cm' and the circumference of its base is
110cm. Find the height and the volume of the cylinder.
3. A cylindrical bucket 28cm in diameter and 72cm high is full of water. The water is
ng and 28cm wide Find the height of the water​

Answer 1

Question 1.

1. The total surface area of a cube 1176 cm² Find its volume.

Answer

★ Volume of cube = 2744 cm³

Explanation :-

Given

• Total surface area of a cube = 1176 cm²

To find

• Volume of the cube

Knowledge required :-

• Formula of total surface area of cube :-

Total surface area of cube = 6 × side²

• Formula of volume of cube :-

⠀⠀⠀Volume of cube = side³

Solution

⠀⠀⠀⇒ T.S.A of cube = 6 × side²

⠀⠀⠀⇒ 1176 = 6 × side²

⠀⠀⠀⇒ 1176/6 × side²

⠀⠀⠀⇒ 196 = side²

⠀⠀⠀⇒ square root on both the sides

⠀⠀⠀⇒ √196 = side

⠀⠀⠀⇒ √(14 × 14) = side

⠀⠀⠀⇒ ± 14 Reject - ve = side

⠀⠀⠀⇒ 14 = side

Side of the cube = 14 cm

⠀⠀⠀⇒ Volume of cube = side³

⠀⠀⠀⇒ Volume of cube = (14)³

⠀⠀⠀⇒ Volume of cube = 2744

Volume of cube = 2744 cm³

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Question 2.

2. The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.

Answer

• Height of the cylinder = 40 cm
• Volume of cylinder = 38,500 cm³

Explanation :-

Given

• Curved surface area of cylinder = 4400 cm²
• Circumference of its base = 110 cm

To find

• Height of the cylinder
• Volume of the cylinder

Knowledge required :-

• Formula of circumference :-

⠀⠀⠀Circumference = 2πr

• Formula of curved surface area of cylinder :-

⠀Curved surface area of cylinder = 2πrh

• Formula of volume of cylinder :-

⠀⠀⠀ Volume of cylinder = πr²h

where,

• Take π = 22/7
• r = radius
• h = height

Solution

⠀⠀⠀⇒ Circumference = 2πr

⠀⠀⠀⇒ 110 = 2 × 22/7 × r

⠀⠀⠀⇒ 110 = 44/7 × r

⠀⠀⠀⇒ 110 × 7/44 = r

⠀⠀⠀⇒ 770/44 = r

⠀⠀⠀⇒ 385/22 = r

⠀⠀⠀⇒ 17.5 = r

Radius = 17.5 cm

⠀⠀⠀⇒ C.S.A of cylinder = 2πrh

⠀⠀⠀⇒ 4400 = 2 × 22/7 × 17.5 × h

⠀⠀⠀⇒ 4400 = 770/7 × h

⠀⠀⠀⇒ 4400 = 110 × h

⠀⠀⠀⇒ 4400/110 = h

⠀⠀⠀⇒ 440/11 = h

⠀⠀⠀⇒ 40 = h

Height of the cylinder = 40 cm

⠀⠀⠀⇒ Volume of cylinder = πr²h

⠀⠀⠀⇒ Volume = 22/7 × 17.5 × 17.5 × 40

⠀⠀⠀⇒ Volume = 38,500

Volume of cylinder = 38,500 cm³

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Question 3.

3. A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water.

Answer

• Height of the water level in the tank = 24 cm

Explanation :-

Given

• Diameter of a cylindrical bucket = 28 cm
• Height of a cylindrical bucket = 72 cm
• Length of the rectangular tank = 66 cm
• Breadth of the rectangular tank = 28 cm

To find

• Height of water in the tank

Knowledge required :-

• Formula of volume of cylinder :-

⠀⠀⠀ Volume of cylinder = πr²h

• Formula of radius :-

⠀⠀⠀Radius = Diameter/2

• Formula of volume of rectangle :-

⠀⠀⠀ Volume of rectangle = l × b × h

where,

• l = length of the rectangle
• b = breadth of the rectangle
• h = height of the rectangle

Solution

⠀⠀⠀⇒ Diameter of cylindrical bucket = 28

⠀⠀⠀⇒ Radius = Diameter/2

⠀⠀⠀⇒ Radius = 28/2

⠀⠀⠀⇒ Radius = 14

Radius of the cylindrical bucket = 14 cm

⠀⠀⠀⇒ Volume of cylindrical bucket = πr²h

⠀⠀⠀⇒ Volume = 22/7 × 14 × 14 × 72

⠀⠀⠀⇒ Volume = 22 × 2 × 14 × 72

⠀⠀⠀⇒ Volume = 44,352

Volume of cylindrical bucket = 44,352 cm³

⠀⠀⠀⇒ Volume of rectangular tank = lbh

⠀⠀⠀⇒ Volume = 66 × 28 × h

⠀⠀⠀⇒ Volume = 1848 × h

Volume of rectangular tank = 1848 × h cm³

According to the question,

⠀⠀⠀⇒ 44,352 = 1848 × h

⠀⠀⠀⇒ 44352/1848 = h

⠀⠀⠀⇒ 24 = h

Height of the water level in the tank = 24 cm

Answer 2

1. Question :

• 1. The total surface area of a cube 1176 cm² Find it's volume.

Given :

• Total surface area of a cube = 1176 cm²

To find :-

• Volume of the cube.

★ Know More Information :

• Formula the total surface area of a cube :

Total surface area of cube = 6 × side²

• Formula of volume of cube :

$~~~~~~~~~~$ Volume of cube = side³

Solution :

$\hookrightarrow$ T.S.A of cube = 6 × side²

$\hookrightarrow$ 1176 = 6 × side²

$\hookrightarrow$ ${\sf{\frac{1176}{6} \times side²}}$

$\hookrightarrow$${\sf{\dfrac{\cancel{1176}}{\cancel{6}} = side²}}$

$\hookrightarrow$ $\large{\underline{\boxed{\red{\bf{196~=~side²}}}}}$★

$\hookrightarrow$ Square root on both the sides

$\hookrightarrow$ $√$196 = side

$\hookrightarrow$ $√$(14 × 14)side

$\hookrightarrow$ $±$14 Reject - Ve = side

$\hookrightarrow$ $\large{\underline{\boxed{\purple{\bf{14~=~side}}}}}$★

Side of the cube = 14 cm

• Volume of cube = side³
• Volume of cube = ( 14 )³
• Volume of cube = 2744

$\large\dag$ Hence,

• Volume of cube = $\underline{\bf{2744~cm³}}$ $\large{\bf\green{✓}}$

________________________________________

2. Question :

• 2. The curved surface area of a cylinder is 4400 cm² and the circumstance of it's base is 110 cm. Find the height and the volume of the cylinder.

Given :-

• Curved surface area of a cylinder = 4400 cm²
• Circumstance of it's base = 110 cm

To find :-

• Height of the cylinder
• Volume of the cylinder

★ Know More Information :

• Formula of circumstance : Circumstance = 2πr

• Formula of curved surface area of cylinder : Curved surface area of cylinder = 2πrh

• Formula of volume of cylinder : Volume of cylinder = πr²h

Where,

• Take $π$ = ${\sf{\frac{22}{7} }}$
• R = radius
• H = height

Solution :

$\hookrightarrow$ Circumstance = 2πr

$\hookrightarrow$ 110 = ${\sf{2 \times \frac{22}{7} \times r}}$

$\hookrightarrow$ ${\sf{110 \times \frac{7}{44} = r}}$

$\hookrightarrow$ ${\sf{ \frac{770}{44} = r}}$

$\hookrightarrow$ ${\sf{\frac{385}{22} = r}}$

$\hookrightarrow$ ${\sf{\dfrac{\cancel{385}}{\cancel{22}} = r}}$

$\hookrightarrow$$\large{\underline{\boxed{\green{\bf{17.5~=~r}}}}}$★

Radius = 17.5 cm

$\hookrightarrow$ C.S.A of cylinder = 2πrh

$\hookrightarrow$ ${\sf{4400 = 2 \times \frac{22}{7} \times 17.5 \times h}}$

$\hookrightarrow$ ${\sf{4400 = \frac{770}{7} \times h}}$

$\hookrightarrow$ ${\sf{4400 = 110 \times h}}$

$\hookrightarrow$ ${\sf{ \frac{4400}{110} = h}}$

$\hookrightarrow$ ${\sf{\frac{440}{11} = h}}$

$\hookrightarrow$ $\large{\sf{\dfrac{\cancel{440}}{\cancel{11}} = h}}$

$\hookrightarrow$ $\large{\underline{\boxed{\green{\bf{40~=~h}}}}}$★

Height of the cylinder = 40 cm

• Volume of cylinder = πr²h
• Volume = ${\sf{ \frac{22}{7} \times 17.5 \times 17.5 \times 40}}$
• Volume = 38,500

$\large\dag$ Hence

• Volume of cylinder = $\underline{\bf{38500~cm³}}$ $\large{\bf\green{✓}}$

________________________________________

3. Question :

• 3. A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is empited into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water.

Given :-

• Diameter of cylindrical bucket = 28 cm
• Height of cylindrical bucket = 72 cm
• Length of the rectangular bucket = 66 cm
• Breadth of the rectangular bucket = 28 cm

To find :-

• Height of water in the tank.

★ Know More Information :

• Formula of volume of cylindrical : Volume of cylindrical = πr²h

• Formula of radius : ${\sf{\frac{Diameter}{2} }}$

• Formula of volume of reactangle : Volume of reactangle = l × b × h

Where,

• L = length of the reactangle
• B = breadth of the reactangle
• H = height of the reactangle

Solution :-

$\hookrightarrow$ Diameter of cylindrical bucket = 28

$\hookrightarrow$ Radius = ${\sf{\frac{Diameter}{2}}}$

$\hookrightarrow$ Radius = ${\sf{\frac{28}{2} }}$

$\hookrightarrow$ Radius = ${\sf{\dfrac{\cancel{28}}{\cancel{2}}}}$

Radius of the cylindrical bucket = 14 cm

• Volume of cylindrical bucket = πr²h
• Volume = ${\sf{\frac{22}{7} \times 14 \times 14 \times 72}}$
• Volume = 22 × 2 × 14 × 72
• Volume = 44,352

Volume of cylindrical bucket = 44,352 cm³

• Volume of reactangle tank = l×b×h
• Volume = 66 × 28 × h
• Volume = 1848 × h

Volume of rectangular tank = 1848 × h

★ According to the question :

$\hookrightarrow$ 44,352 = 1848 × h

$\hookrightarrow$ ${\sf{\frac{44352}{1848} = h}}$

$\hookrightarrow$ ${\sf{\dfrac{\cancel{44352}}{\cancel{1848}} = h}}$

$\hookrightarrow$$\large{\underline{\boxed{\bf{\pink{24~=~h}}}}}$★

$\large\dag$ Hence

• Height of the water level in the tank = $\underline{\bf{24~cm}}$ $\large{\bf\green{✓}}$