Surface Areas and Volumes — Flashcards
Gujarat Board · Class 9 · Mathematics
24 flashcards for Surface Areas and Volumes (Gujarat Board Class 9 Mathematics) to test yourself on key terms and facts.
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What is a right circular cone? How is it formed?
Answer
A right circular cone is a solid figure formed when a right-angled triangle is rotated about one of its perpendicular sides. The vertex is the pointed top, the height is the perpendicular distance fro…
What is the formula for the curved surface area of a cone?
Answer
Curved Surface Area of a Cone = πrl, where r is the base radius and l is the slant height. This formula represents the area of the curved surface only, not including the base.
What is the formula for the total surface area of a cone?
Answer
Total Surface Area of a Cone = πrl + πr² = πr(l + r), where r is the base radius and l is the slant height. This includes both the curved surface area (πrl) and the area of the circular base (πr²).
How do you find the slant height of a cone when given height and radius?
Answer
Use the Pythagorean theorem: l² = r² + h², so l = √(r² + h²), where l is slant height, r is base radius, and h is the height of the cone.
Find the curved surface area of a cone with base radius 7 cm and slant height 10 cm.
Answer
Curved Surface Area = πrl = (22/7) × 7 × 10 = 22 × 10 = 220 cm²…
What is a sphere and how is it formed?
Answer
A sphere is a three-dimensional solid figure made up of all points in space that lie at a constant distance (radius) from a fixed point (center). It is formed when a circular disc is rotated about its…
What is the formula for the surface area of a sphere?
Answer
Surface Area of a Sphere = 4πr², where r is the radius of the sphere. This formula gives the total surface area of the sphere.
What is a hemisphere and what are its surface area formulas?
Answer
A hemisphere is half of a sphere, formed by cutting a sphere through its center. Curved Surface Area = 2πr² (half of sphere's surface area). Total Surface Area = 3πr² (curved surface + flat circular b…
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