Question

volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height.( π=3.14)​

Answer 1

☆Answer☆

Given:-

• Volume of cone = 6280 cm³
• Base radius of the cone = 30 cm

To Find:-

• Perpendicular Height of the cone

Solution:-

Let the Perpendicular height of the cone be 'h' cm.

Radius of the base, r = 30 cm

Volume of the cone = 6280 cm³

πr²h/3 = 6280 cm³

(1/3) × 3.14 × (30) × h = 6280 cm³

=> h = (6280×3)/(3.14×900)

On further solving, we get:

h = 6.67 cm (approx)

Thus, the perpendicular height of the cone is 6.67 cm.

✔

Answer 2

Answer:

6.67 ᴄᴍ

Step-by-step explanation:

$\blue{ \bf{ \underline{QUESTION} : }}$

Volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height.

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$\boxed{ \huge{ \bold{ Given}}}$

• Volume of the Cone = 6280 cm³

• Radius (r) = 30 cm

$\boxed {\huge{ \bold{ to \: find}}}$

• Height of the Cone

$\star{ \pink{ \underline{ \underline{ｓｏｌｕｔｉｏｎ : - }}}}$

We Know ➦

$\boxed{ \boxed{ \red{ \sf{Volume \: of \: the \: Cone \: = \frac{1}{3}}\pi {r}^{2}h }}}$

$\: \: \: \: \: \: \: \:$

$\: \: \: \: \: \: {: {\implies{ \sf{6280 = \frac{1}{3} \times 3.14 \times {30}^{2} \times h \: \: \: \: }}}}$

$\: \: \: \: \: \: \: \:$

$\: \: \: \: \: \: {: {\implies{ \sf{6280 = \frac{1}{ \cancel3} \times 3.14 \times \cancel {900 } \times h \: \: \: \: }}}}$

$\: \: \: \: \: \: {: {\implies{ \sf{6280 = 3.14 \times 300 \times h \: \: \: \: }}}}$

$\: \: \: \: \: \: {: {\implies{ \sf{6280 = 942 \times h \: \: \: \: }}}}$

$\: \: \: \: \: \: {: {\implies{ \sf{ \cancel \frac{6280}{942} = h \: \: \: \: }}}}$

$\: \: \: \: \: \: {: {\implies{ \sf{ \boxed{ \frak{ \red{6.67 \: cm = { h \: \: \: \: }}}}}}}}$

$\therefore {\bold{Height = 6.67 cm }}$

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More You Know ➥

• The volume of a cylinder = Area of the base × Height of the cylinder = πr²h

• Lateral Surface Area = Perimeter of base × height = 2πrh = πdh

• Total Surface Area = Lateral Surface Area + Area of bases = 2πrh + 2πr² = 2πr (h+r)

• Volume of Hollow Cylinder = Vol of External Cylinder – Vol of Internal Cylinder = πR²h – πr²h = π (R² – r²) h

• Lateral Surface (hollow cylinder) = External Surface Area + Internal Surface Area = 2πRh + 2πrh = 2π(R+r)h

• Total Surface Area (cylinder) = Lateral Area = Area of bases = 2π(R+r)h + 2π (R² – r²) h

• Volume of Cone = 1/3 π r² h

• Lateral Surface = πrl

• where l = slant height = √(r²+ h² )

• Total Surface Area = πrl + π r²

• Surface Area of a Sphere = 4 times

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