Question

Two cones have their base radii in ratio of 5 : 1 and the ratio of their heights as 1 : 5. Find the ratio of their volumes? ​

Answer 1

$\huge \bf \color{green} \mathfrak{Question : - }$

• Two cones have their base radii in ratio of 5 : 1 and the ratio of their heights as 1 : 5. Find the ratio of their volumes ?

$\huge \bf \color{blue} \mathfrak{Solution : - }$

Let's,

The Radius of First Cone (r) = 5X

So,

The Radius Of Second Cone (R) = X

Let's,

The Height Of First Cone (h) = X

So,

The Height Of Second Cone (H) = 5X

Volume of First Cone = ⅓ × π × r² × h

→ Volume of First Cone = ⅓ × π × (5X)² × (X)

→ Volume of First Cone = ⅓ × π × 25X² × X

→ Volume of First Cone = ⅓ × π × 25X³

Volume of Second Cone = ⅓ × π × R² × H

→ Volume of Second Cone = ⅓ × π × (X)² × (5X)

→ Volume of Second Cone = ⅓ × π × X² × 5X

→ Volume of Second Cone = ⅓ × π × 5X³

The Ratio Of Their Volumes = Volume of First Cone / Volume Of Second Cone

→ The Ratio Of Their Volumes

= (⅓ × π × 25X³)/(⅓ × π × 5X³)

→ The Ratio Of Their Volumes = 5 : 1

$\huge \bf \color{orange} \mathfrak{Answer : - }$

The Ratio Of Their Volumes = 5 : 1