Seshu cheera

Class 10 CBSE Maths Chapter 13: Surface Areas and Volumes , including: ✅ Key Concepts & Formulas 📘 All NCERT Exercise Questions with detailed solutions 📝 CBSE Previous Year Questions from this chapter 📚 Chapter 13: Surface Areas and Volumes This chapter explores the curved surface area (CSA) , total surface area (TSA) , and volume of 3D solids, including cylinders , cones , spheres , hemispheres , frustums , and composite solids . 🧠 Key Concepts and Formulas 🔸 1. Right Circular Cylinder Let r r = radius, h h = height CSA = 2 π r h 2\pi rh TSA = 2 π r ( h + r ) 2\pi r(h + r) Volume = π r 2 h \pi r^2 h 🔸 2. Right Circular Cone Let r r = radius, h h = height, l l = slant height Where l = r 2 + h 2 l = \sqrt{r^2 + h^2} CSA = π r l \pi r l TSA = π r ( l + r ) \pi r(l + r) Volume = 1 3 π r 2 h \frac{1}{3} \pi r^2 h 🔸 3. Sphere Let r r = radius Surface Area = 4 π r 2 4\pi r^2 Volume = 4 3 π r 3 \frac{4}{3} \pi r...

✅ Class 10 Maths Chapter 12: Areas Related to Circles 📚 Chapter Overview: This chapter helps students apply the properties of circles to find the area and perimeter (circumference) of sectors , segments , and composite figures involving circles. It blends geometry and mensuration skills for real-life applications. 🧠 Key Concepts, Formulas, and Theorems: 🔹 1. Circle: A closed two-dimensional figure where all points are equidistant from a fixed point (center). Radius (r): Distance from center to any point on the circle. Diameter (d): Twice the radius, i.e., d = 2 r d = 2r Circumference: Total boundary length of the circle Circumference = 2 π r \text{Circumference} = 2\pi r 🔹 2. Area of a Circle: Area = π r 2 \text{Area} = \pi r^2 Where π = 22 7  or  3.14 \pi = \frac{22}{7} \text{ or } 3.14 🔹 3. Sector of a Circle: A sector is a portion of a circle enclosed by two radii and the arc between them. Area of Sector : θ 360 ∘ × π r 2 \frac{\th...