Question

Two similar solids have heights of 6 cm and 9 cm. If the volume of the smaller solid is 88 ${cm}^{3}$, calculate the volume of the larger solid.​

Answer 1

Given :-

• Height of smaller solid = 6cm
• Height of larger solid = 9cm
• Volume of smaller solid = 88cm³

To Find :-

• The volume of larger solid = ?

Solution :-

• To calculate the volume of larger solid at first we have to assume the shape of similar solids be cylinder. As given in the question two similar solids with different heights but similar for its radius. It means here we have to find out the radius of cylinder by applying formula. Then calculate the volume of larger solid.

Formula Used :-

⇒ Volume of smaller Cylinder = π × r² × h

⇒ 22/7 × r² × 6 = 88

⇒ 22 × 6 × r² = 88 × 7

⇒ 6 × r² = 4 × 7

⇒ r² = 28/6

⇒ r² = 14/3

⇒ r = √14/3

• Now calculate the volume of larger solid :-

Now we have here :-

• Height = 9cm. r = √14/3

⇒ Volume of larger solid = π × r² × h

⇒ Volume = 22/7 × (√14/3)² × 9

⇒ Volume = 22/7 × 14/3 × 9

⇒ Volume = 22 × 2 × 3

⇒ Volume = 132cm³

Hence,

• The volume of larger solid = 132cm³

Answer 2

Given :-

Two similar solids have heights of 6 cm and 9 cm. If the volume of the smaller solid is 88 cm²

To Find :-

Calculate the volume of the larger solid.​

Solution :-

Here, Height and Volume are in proportion

This means

H₁/H₂ = V₁/V₂

Let the larger volume be x

6/9 = 88/x

9/6 × 88= x

x = 792/6

x = 132 cm³