Question

Given two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.

How much more water can the second cone hold than the first cone? Round your
answer to the nearest hundredth.

603.19 in.3

753.98 in.3

1,357.17 in.3

1,960.36 in.3

Answer 1

• 753.98 in³

Step-by-step Step-by-step explanation:

According to the question It's given that :

Two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.

Here,

• Radius of 1st cone = 8 inches
• Radius of 2nd cone = 12 inches

Since, Both the cones are of the same height.

• Height of 1st cone = 9 inches
• Height of 2nd cone = 9 inches

Formula of volume of cone = 1/3 πr²h

where,

• π = 3.14
• r = radius
• h = height

For first cone,

`\implies` Volume = 1/3 × 3.14 × (8)² × 9

`\implies` 1/3 × 3.14 × 64 × 9

`\implies` 1/3 × 3.14 × 576

`\implies` 1/3 × 1808.64

`\implies` 602.88 in³

For second cone,

`\implies` Volume = 1/3 × 3.14 × (12)² × 9

`\implies` 1/3 × 3.14 × 144 × 9

`\implies` 1/3 × 3.14 × 1296

`\implies` 1/3 × 4069.44

`\implies` 1356.48 in³

Now, How much more water can the second cone hold than the first cone?

Volume of 2nd cone - Volume of 1st cone

`\implies` 1356.48 - 602.88

`\implies` 753 (approximately)

Therefore, 753.98 in³ is the answer .