Question

a container made up of metal sheet is the form of a frustrum of a cone of height 16cm with radii of its lower and upper ends 8cm and 20cm respectively find the amount of liquid the container can hold is​

Answer 1

Answer:

The amount of liquid the container can hold = 10.45 litre

Step-by-step explanation:

Given:

• Height of a container, h = 16 cm
• Radius of lower end of a container, r = 8 cm
• Radius of upper end of a container, R = 20 cm

To find:

• The amount of liquid the container can hold.

Solution:

✰ Slant height of frustum = √( R - r)² + h²

Here,

R = Radius of upper end of a container.

r = Radius of lower end of a container

h = Height of a container

• Slant height of frustum = √(20 - 8)² + 16²
• Slant height of frustum = √12² + 16²
• Slant height of frustum = √144 + 256
• Slant height of frustum = √400
• Slant height of frustum = 20 cm

The amount of liquid the container can hold is nothing but the capacity of container which is equal to the volume of frustum.

Volume of frustum = 1/3π( R² + r² + Rr )h

Putting the values in the formula, we have:

• Volume of frustum = 1/3 × 22/7 × ( 20² + 8² + 20 × 8 ) × 16
• Volume of frustum = Volume of frustum = 1/3 × 22/7 × ( 400 + 16 + 20 × 8 ) × 16
• Volume of frustum = Volume of frustum = 1/3 × 22/7 × ( 400 + 16 + 160 ) × 16
• Volume of frustum = Volume of frustum = 1/3 × 22/7 × 624 × 16
• Volume of frustum = 10449.92 cm³
• Volume of frustum = 10449.92/1000 l
• Volume of frustum = 10.44992 l
• Volume of frustum = 10.45 litre

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