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: Identify given values.
Radius \(r = 7\) cm, slant height \(l = 25\) cm. We need the Total Surface Area (TSA) of the solid cone.
Step 2: Recall the TSA formula for a cone.
\(\text{TSA} = \pi r l + \pi r^2 = \pi r(l + r)\).
Step 3: Substitute the values.
\(\text{TSA} = \frac{22}{7} \times 7 \times (25 + 7) = 22 \times 32\).
Step 4: Compute the product.
\(22 \times 32 = 704\) cm\(^2\).
Step 5: Verify the calculation.
Curved surface area \(= \pi r l = \frac{22}{7} \times 7 \times 25 = 550\) cm\(^2\). Base area \(= \pi r^2 = \frac{22}{7} \times 49 = 154\) cm\(^2\). Total \(= 550 + 154 = 704\) cm\(^2\).
Step 6: Select the correct option.
TSA \(= 704\) cm\(^2\), which is option 2.
\[ \boxed{704 \text{ cm}^2} \]