Question

the area of base of a right circular cylinder is 15400 cm square and its volume is 92400 cm cube find the height of the cylinder and also find the curved surface of the cylinder

Answer 1

$\textbf{\huge{ANSWER:}}$

$\sf{We're \:Given\:that:}$

Area of the base of the cylinder = 15400 cm^2

Volume of the cylinder = 92400 cm^3

Let's divide this question into 3 parts, one in which we'll find the radius, second in which we'll find the Height, and at last we'll find the Curved Suface area (C.S.A.) of the cylinder.

$\tt{Part \:I}$

Area = $\pi r^{2}$

=》 15400 = $\frac{22}{7}\times r^{2}$

=》 $r^{2}$ = 4900

=》 $\tt{\boxed{r = 70 cm}}$

$\sf{Part \:II}$

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

=》 92400 = $\frac{22}{7} \times 70 \times 70\times h$

=》 h = $\frac{92400\times7}{70\times 70\times22}$

=》 $\tt{\boxed{h = 6 cm}}$

$\sf{Part \:III}$

C.S.A. = $2\pi r h$

=》 $2 \times \frac{22}{7} \times 70 \times 6$

=》 $\tt{\boxed{C.S.A. = 2640 cm^{2}}}$

We've solved all the parts now by just using the formulae we knew from the very starting !

Answer 2

Given :

Area of the base of a right circular cylinder = 15400 cm² .

We know that the base of the cylinder is a circle.

Hence the area of the circle is 15400 cm² .

Let radius of the base be r .

π r² = 15400 cm²

⇒ 22/7 × ( r )² = 15400 cm²

⇒ r² = 15400 × 7/22

⇒ r² = 700 × 7

⇒ r² = 4900

⇒ r = √4900

⇒ r = 70 ..........( 1 )

This means that the radius of the cylinder = 70 cm .

Volume of cylinder = 92400 cm³ .

Formula for volume = π r² h

⇒ 22/7 × 70² × h = 92400 cm³

⇒ 22/7 × 4900 × h = 92400 cm³

⇒ h = 92400 / 22 × 7/4900

⇒ h = 4200 × 7/4900

⇒ h = 6 cm

The height is 6 cm

Curved surface area = 2 π r h

= > 2 × 22/7 × 70 × 6

⇒ 2 × 22 × 10 × 6

⇒ 440 × 6

⇒ 2640 cm²

The curved surface area is 2640 cm²