Finding the Lateral Surface Area of a Cone
This solution explains how to calculate the lateral surface area of a right circular cone using the given diameter and slant height.
Given Information:
- Diameter of the base, $d = 8$ cm
- Slant height, $l = 14$ cm
- Value of $\pi = \frac{22}{7}$
Step 1: Determine the Radius
The radius ($r$) of the circular base is half its diameter ($d$).
Calculation: $r = \frac{d}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}$
Step 2: Calculate Lateral Surface Area (LSA)
The formula for the lateral surface area of a right circular cone is:
$LSA = \pi \times r \times l$
Substitute the known values into the formula:
$LSA = \frac{22}{7} \times 4 \text{ cm} \times 14 \text{ cm}$
Perform the multiplication:
$LSA = 22 \times 4 \text{ cm} \times \frac{14}{7} \text{ cm}$
Simplify by dividing 14 by 7:
$LSA = 22 \times 4 \text{ cm} \times 2 \text{ cm}$
Continue multiplying:
$LSA = 88 \text{ cm} \times 2 \text{ cm}$
$LSA = 176 \text{ cm}^2$
Result
The calculated lateral surface area of the cone is $176 \text{ cm}^2$.
Similar Questions
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Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
