A cone has a radius of 2 cm and a height of 9 cm. What is its volume?

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Question: A cone has a radius of 2 cm and a height of 9 cm. What is its volume?

Options:

Correct Answer: 18π cm³

Solution:

Volume = 1/3 × πr²h = 1/3 × π × (2 cm)² × 9 cm = 12π cm³.

A cone has a radius of 2 cm and a height of 9 cm. What is its volume?

A cone has a radius of 2 cm and a height of 9 cm. What is its volume?

Step 1: Identify the formula for the volume of a cone, which is Volume = 1/3 × π × r² × h.
Step 2: Identify the values needed for the formula. The radius (r) is 2 cm and the height (h) is 9 cm.
Step 3: Calculate r² (the radius squared). Since r is 2 cm, r² = (2 cm) × (2 cm) = 4 cm².
Step 4: Substitute the values into the volume formula: Volume = 1/3 × π × 4 cm² × 9 cm.
Step 5: Multiply 4 cm² by 9 cm to get 36 cm³.
Step 6: Now substitute this back into the formula: Volume = 1/3 × π × 36 cm³.
Step 7: Calculate 1/3 of 36 cm³, which is 12 cm³.
Step 8: Finally, write the volume as Volume = 12π cm³.

Volume of a Cone – The formula for the volume of a cone is V = 1/3 × πr²h, where r is the radius and h is the height.
Substitution and Calculation – Correctly substituting the values of radius and height into the formula and performing the calculations accurately.