A cone has a radius of 3 cm and a height of 4 cm. What is its volume?

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Question: A cone has a radius of 3 cm and a height of 4 cm. What is its volume?

Options:

Correct Answer: 12π cm³

Solution:

Volume = 1/3 × πr²h = 1/3 × π × (3 cm)² × 4 cm = 12π cm³.

A cone has a radius of 3 cm and a height of 4 cm. What is its volume?

A cone has a radius of 3 cm and a height of 4 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 radius (r) and height (h) of the cone. Here, r = 3 cm and h = 4 cm.
Step 3: Calculate r² (the radius squared). So, (3 cm)² = 9 cm².
Step 4: Substitute r² and h into the volume formula: Volume = 1/3 × π × 9 cm² × 4 cm.
Step 5: Multiply 9 cm² by 4 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.