Question

The area of the base of a right circular cone is 78.5cm^2. If its height is 12cms, then its volume is

Answer 1

Answer:

Ginven,area of the base of right circular cone

= 314 cm^2

since, we know that base of right circular cone is circular . so then

area of the base = area of circle = πr^2

Find the radius:

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πr^2 = 314 cm^2

r^2 = 314 × ( 7 / 22 )

r^2 = 2198 ÷ 22 = 99.9 = 100 cm

r = √100 = 10 cm

radius of right circular cone = 10cm

given , height of the cone = 15 cm

Find the volume:

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volume of the cone = (πr^2h / 3)

= (π × ( 10 )^2 × 15 ) / 3

= (22/ 7 ) × ( 100 × 5 )

=( 22× 500 ) ÷ 7 = 11000 ÷ 7

= 1571.4 cm^3

therefore, volume of the right circular cone = 1571.4 cm^3

Answer: volume = 1571.4 cm^3

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

${\boxed{\sf\:{Area\;of\;Base}}}$

= 78.5 cm²

Hight (h)

= 12 cm

Assumption

Radius be "r cm"

Also,

Slant height = l cm

As we know that :-

Area of base = πr²

78.5 = 3.14 × r²

$\tt{\rightarrow r^2=\dfrac{78.5}{3.14}}$

$\tt{\rightarrow r^2=\dfrac{7850}{314}}$

r = √25

r = 5

$\tt{\rightarrow Volume\;of\;Cone=\dfrac{1}{3}\times\pi r^2h}$

$\tt{\rightarrow\dfrac{1}{3}\times 3.14\times(5)^2\times 12}$

= 3.14 × 25 × 4

= 314 cm³

∴ The volume of the cone is 314 cm³.