Question

The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is

• A. \(724\text{ cm}^2\)
• B. \(704\text{ cm}^2\)
• C. \(550\text{ cm}^2\)
• D. \(616\text{ cm}^2\)

Hint:

Using the factored formula \(\pi r(l+r)\) instead of calculating \(\pi r l\) and \(\pi r^2\) separately saves significant calculation time and prevents rounding errors.
The direct cancellation of 7 makes the math very straightforward!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question is from the topic Surface Areas and Volumes.
We are given a solid cone with a radius of \(7\text{ cm}\) and a slant height of \(25\text{ cm}\).
We need to compute its total surface area (TSA), which includes both the curved surface area and the circular base area.

Step 2: Key Formula or Approach:
The total surface area (TSA) of a solid cone is the sum of its Curved Surface Area (CSA) and the Area of its circular base.
- \(\text{Curved Surface Area} = \pi r l\)
- \(\text{Base Area} = \pi r^2\)
- \(\text{Total Surface Area (TSA)} = \pi r l + \pi r^2 = \pi r(l + r)\)
where: - \(r\) is the radius of the base.
- \(l\) is the slant height of the cone.

Step 3: Detailed Explanation:
1. Write down the given dimensions: - Radius of the cone, \(r = 7\text{ cm}\)
- Slant height, \(l = 25\text{ cm}\)
- Constant, \(\pi = \frac{22}{7}\)
2. Apply the formula for the Total Surface Area: \[ \text{TSA} = \pi r (l + r) \] 3. Substitute the values of \(r\), \(l\), and \(\pi\) into the formula: \[ \text{TSA} = \frac{22}{7} \times 7 \times (25 + 7) \] 4. Simplify the expression by cancelling the 7 in the numerator and denominator: \[ \text{TSA} = 22 \times (25 + 7) \] \[ \text{TSA} = 22 \times 32 \] 5. Calculate the final product: \[ 22 \times 32 = 22 \times (30 + 2) = 660 + 44 = 704\text{ cm}^2 \]

Step 4: Final Answer:
The total surface area of the solid cone is \(704\text{ cm}^2\).
Therefore, the correct option is (B).