Question

The height of a right circular cone is 35cm and the area of its curved surface is four times the

area of its base. What is the volume of the cone (in 10-3 m3

) ?​

Answer 1

The volume of the cone is 3 * 10⁻³ m³.

Step-by-step explanation:

Step 1:

It is given that,

The area of the curved surface of a cone = four times the area of the base of the cone

⇒ πrl = 4 * πr²

Cancelling the similar terms

⇒ l = 4r …. (i)

Step 2:

The height of the right circular cone, h = 35 cm

We know that the slant height of the cone is given by,

l² = h² + r²

substituting l = 4r from (i) and h = 35 cm

⇒ (4r)² = 35² + r²

⇒ 16r² = 1225 + r²

⇒ 15r² = 1225

⇒  r² = $\frac{1225}{15}$

⇒ r² = 81.67 cm ..... (ii)

Step 3:

Therefore,

The volume of the cone is given by,

= $\frac{1}{3}$ πr²h

= $\frac{1}{3} * \frac{22}{7}$ * 81.67 * 35 ..... [substituting from (ii)]

= 2994.56 cm³

= 2994.56 * 10⁻⁶

= 2.99 * 10⁻³

≈ 3 * 10⁻³ m³

Thus, the volume of the cone in m³ is 3 * 10⁻³ m³.

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Answer 2

The volume of the cone is $V=3\times 10^{-3}\ m^3$.

Step-by-step explanation:

Given : The height of a right circular cone is 35cm and the area of its curved surface is four times the  area of its base.

To find : What is the volume of the cone ?

Solution :

Area of the curved surface of cone = 4 times the area of base of cone

i.e. $\pi r l = 4\times \pi r^2$

$l=4r$

The slant height formula is $l^2=h^2+r^2$

Substituting, l = 4r

$(4r)^2=35^2+r^2$

$16r^2=1225+r^2$

$15r^2=1225$

$r^2=81.6$

Volume of cone is $V=\frac{1}{3}\pi r^2 h$

$V=\frac{1}{3}\times \frac{22}{7}\times 81.6\times 35$

$V=2994.42\ cm^3$

Convert into m³,

$1\ cm^3=10^{-6}\ m^3$

$V=2994.42\times 10^{-6}\ m^3$

$V=2.99\times 10^{-3}\ m^3$

Therefore, the volume of the cone is $V=3\times 10^{-3}\ m^3$.

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