Question

please give me answers 6,7,8,9 ! please​

Answer 1

Answer:

1. The volume and area of curved surface of a right circular cylinder are 1540 m³ and 440m² respectively. Find the radius of the base and the height of the cylinder.

Given :

• Volume of Cylinder → 1540 m³
• Curved Surface Area → 440 m²

Find :

• Find the radius of the base and the height of the cylinder.

Solution :

As we know ,

Formulas :-

$\boxed{\bf{C.S.A = 2 \pi rh}}$

$\boxed{\bf{Volume = \pi r^{2}h}}$

From given -

$:\implies\sf{Curved \: Surface \: Area = 440m^{2}}$

$:\implies\sf{2 \pi rh = 440m^{2}}$

$:\implies\sf{ \pi rh = \dfrac{440}{2}}$

$:\implies\sf{ \pi rh = 220}$

Now,

We know

$\boxed{\sf{Volume = \pi r^{2}h}}$

πr²h = πr × r × h

Putting πrh as 220

$:\implies\sf{220 \times r = 220r}$

From the above data :

→ 220r = 1540 m³

r = 1540/220

r = 7m

Subscribe the value of " r " to find the height :

πr²h = 1540

→ 22/7 × (7)² × h = 1540

→ 22 × 7 × h = 1540

→ h = 1540 / 7 × 22

→ h = 1540/154

→ h = 10 m

Hence, Radius of cylinder is 7 m and height of cylinder is 10 m.

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2. The total surface area of a right circular cylinder is 264 m² if the sum of its base and height is 10 find height.

Given :

• Total surface area of a right circular cylinder is 264 m²
• The sum of its base and height is 10.

Find :

• Find the height.

Solution :

As we know ,

Formulas :-

$\boxed{\bf{T.S.A = 2 \pi r(r +h)}}$

Substituting the values in it, we get :

→ 2πr × 10 = 264

→ 2 × 22/7 × r × 10 = 264

→ r = 264 × 7/22 × 2 × 10

→ r = 264 × 7/44 × 10

→ r = 1848/440

→ r = 4.2 m

Now , For height

Sum of base radius and Height → 10 m

→ 4.2 + h = 10

→ h = 10 - 4.2

→ h = 5.8m

Hence , the height is 5.8 m.

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3. Two right circular cylinders of equal volume are such that their radii are in the ratio 4: 5 . Find the ratio of their heights.

Given :

• Two right circular cylinders of equal volume.
• Radii are in the ratio 4: 5.

Find :

• Find the ratio of their heights.

Solution :

As we know ,

$\boxed{\bf{Volume = \pi r^{2}h}}$

Let's we consider the unknown ratio of heights be H : h

Refer to the Attachment for further calculations.

___________________________

4. A metal cube of side 6 cm is melted and formed into three smaller cubes. If the sides of two smaller cubes are 3 cm , and 5 cm . find the side of third smaller cube.

Given :

• Side of bigger cube - 6 cm
• Side of two smaller cube - 3 and 5 cm respectively.

Find :

• Find the side of third smaller cube.

As we know that Volume of big cube will be equal to the volume of 3 small cubes.

For Volume of big cube -

$\boxed{\bf{Volume = Side^{3}}}$

$:\implies\sf{Volume = 6^{3}}$

$:\implies\sf{Volume = 216cm^{3}}$

Now, Volume of small cubes -

Cube 1 :

$\boxed{\bf{Volume = Side^{3}}}$

$:\implies\sf{Volume = 3^{3}}$

$:\implies\sf{Volume = 27cm^{3}}$

Cube 2 :

$\boxed{\bf{Volume = Side^{3}}}$

$:\implies\sf{Volume = 5^{3}}$

$:\implies\sf{Volume = 125cm^{3}}$

Now, Volume of 3rd smaller cube = (Volume of big cube - Volume Sum of two smaller cube)

→ 216 - ( 125 + 27)

→ 216 - ( 152 )

→ 64 cm³

Now,

$:\implies\sf{Volume = Side^{3}}$

$:\implies\sf{Side^{3} = 64}$

Side = √64

$\boxed{\bf{Side = 4cm}}$

_________________________

Answer 2

6. The volume and area of curved surface of a right circular cylinder are 1540 m³ and 440m² respectively. Find the radius of the base and the height of the cylinder.

Given :

Volume of Cylinder → 1540 m³

Curved Surface Area → 440 m²

Find :

Find the radius of the base and the height of the cylinder.

$\huge \sf{ \underline{ \underline{Solution : }}}$

$\rightarrow \: \sf{Curved \: Surface \: Area = 440m^{2}}$

$\rightarrow\sf{2 \pi rh = 440m^{2}}$

$\rightarrow\sf{ \pi rh = \dfrac{440}{2}}$

$\rightarrow\sf{ \pi rh = 220}$

Now,

$\purple{\boxed{\sf{Volume = \pi r^{2}h}}}$

$\purple{ \boxed{πr²h = πr × r × h }}$

Putting πrh as 220

$\rightarrow\sf{220 \times r = 220r}$

→ 220r = 1540 m³

$\boxed{r = \frac{1540}{220}}$

$\sf \: r = 7m$

Substitute the value of " r " to find the height :

πr²h = 1540

$\sf \frac{ 22}{7 }× (7)² × h = 1540$

$\sf 22 × 7 × h = 1540$

$\sf h = \frac{ 1540 }{7 }× 22$

$\sf \: h = \frac{ 1540}{154}$

$\sf \: h = 10 m$

Hence, Radius of cylinder is 7 m and height of cylinder is 10 m.

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Question 7

The total surface area of a right circular cylinder is 264 m² if the sum of its base and height is 10 find height.

Given :

Total surface area of a right circular cylinder is 264 m²

The sum of its base and height is 10.

Find :

Find the height.

Solution :

Substituting the values in it, we get :

=》 2πr × 10 = 264

$\boxed{ \sf \: 2 × \frac{22}{7} × r × 10 = 264 }$

$\boxed{ \sf r = 264 × \frac{7}{22 }× 2 × 10}$

$\sf \: r = 264 × \frac{7}{44} × 10$

$\boxed{ \sf{ r = \frac{1848}{440}}}$

$\pink{ \boxed{ \sf{ r = 4.2 m }}}$

Now , For height

Sum of base radius and Height → 10 m

=》4.2 + h = 10

=》h = 10 - 4.2

=》 h = 5.8m

Hence , the height is 5.8 m.

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8.Two right circular cylinders of equal volume are such that their radii are in the ratio 4: 5 . Find the ratio of their heights.

Given :

Two right circular cylinders of equal volume.

Radii are in the ratio 4: 5.

Find :

Find the ratio of their heights.

Solution :

As we know ,

$\star \: {\bf{Volume = \pi r^{2}h}}$

Refer to the Attachment for answers.

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9. A metal cube of side 6 cm is melted and formed into three smaller cubes. If the sides of two smaller cubes are 3 cm , and 5 cm . find the side of third smaller cube.

Given :

Side of bigger cube - 6 cm

Side of two smaller cube - 3 and 5 cm respectively.

Find :

Find the side of third smaller cube.

As we know that Volume of big cube will be equal to the volume of 3 small cubes.

For Volume of big cube -

$\star \: {\bf{Volume = Side^{3}}}$

$\rightarrow \sf{Volume = 6^{3}}$

$\rightarrow\sf{Volume = 216cm^{3}}$

Now, Volume of small cubes -

Cube 1 :

$\pink \star \: \boxed{\bf{Volume = Side^{3}}}$

$\boxed{\implies\sf{Volume = 3^{3}}}$

$\implies\sf{Volume = 27cm^{3}}$

Cube 2 :

$\boxed{\bf{Volume = Side^{3}}}$

$\implies\sf{Volume = 5^{3}}$

$\boxed{\implies\sf{Volume = 125cm^{3}}}$

Now, Volume of 3rd smaller cube = (Volume of big cube - Volume Sum of two smaller cube)

=》216 - ( 125 + 27)

=》 216 - ( 152 )

=》 64 cm³

Now,

$\boxed{\implies\sf{Volume = Side^{3}} }$

$\rightarrow\sf{Side^{3} = 64}$

$\purple \dag \: { \boxed{ \bf{Side = \sqrt{64} }}}$

$\huge \boxed{ \sf \: side = 4cm}$

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