A20 cm
B40 cm
C30 cm
D50 cm
Answer:
B. 40 cm
Read Explanation:
Key Concepts for Solids: Cones
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.
Radius (r): The distance from the center of the base to any point on the circumference of the base.
Height (h): The perpendicular distance from the apex to the center of the base.
Slant Height (l): The distance from the apex to any point on the circumference of the base. It is related to the radius and height by the Pythagorean theorem: l² = r² + h².
Curved Surface Area (CSA): The area of the slanted surface of the cone. Formula: CSA = πrl.
Total Surface Area (TSA): The sum of the curved surface area and the area of the base. Formula: TSA = CSA + Base Area = πrl + πr² = πr(l + r).
Problem Breakdown and Solution Approach
Given:
Radius of the cone (r) = 10 cm
Ratio of Curved Surface Area (CSA) to Total Surface Area (TSA) = 4:5
To Find: Slant height (l) of the cone.
Using the Formulas:
CSA = πrl
TSA = πr(l + r)
Applying the Ratio:
CSA / TSA = (πrl) / (πr(l + r)) = 4/5
Simplifying the Equation:
l / (l + r) = 4/5
Cross-multiplication:
5l = 4(l + r)
5l = 4l + 4r
Solving for l:
5l - 4l = 4r
l = 4r
Substituting the value of r:
l = 4 × 10 cm
l = 40 cm