Class 10th Surface Areas and Volumes One ShotClass 10 Maths Chapter 12 | ( Ex. 12.1 + 12.2)

Описание: 📚 Class 10 Maths - Surface Area and Volume | Complete Chapter in One Video

Welcome to this one-shot video on Surface Area and Volume from Class 10 Mathematics! This video covers all important concepts, formulas, and NCERT questions with step-by-step explanations.

📖 Topics Covered in This Video:

✔️ Surface Area & Volume of Different Shapes (Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere)
✔️ Combination of Solids
✔️ Conversion of Solids from One Shape to Another
✔️ Frustum of a Cone
✔️ Important Formulas & Tricks
✔️ NCERT & Previous Year Questions Solved

📌 NCERT Questions Covered in This Video:

Exercise 12.1 (Surface Area)

1️⃣ Two cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.
2️⃣ A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm, and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
3️⃣ A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
4️⃣ A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
5️⃣ A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
6️⃣ A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the capsule is 14 mm, and the diameter is 5 mm. Find its surface area.

Exercise 12.2 (Volume)

1️⃣ A solid is in the shape of a cone standing on a hemisphere with both having the same radius (1 cm), and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
2️⃣ Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its ends using a thin aluminum sheet. The diameter of the model is 3 cm, and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.
3️⃣ A gulab jamun contains sugar syrup up to 30% of its volume. Find approximately how much syrup would be in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends, having a length of 5 cm and diameter of 2.8 cm.
4️⃣ A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each conical depression is 0.5 cm, and the depth is 1.4 cm. Find the volume of wood in the entire stand.
5️⃣ A vessel is in the form of an inverted cone with height 8 cm and radius 5 cm. It is filled with water up to the brim. When lead shots (spheres of radius 0.5 cm) are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
6️⃣ A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole if 1 cm³ of iron weighs 8 g. (Use π = 3.14)
7️⃣ A solid consisting of a cylinder (height 120 cm, radius 60 cm) stands on a hemisphere (radius 60 cm) and is placed in a larger cylinder (radius 60 cm, height 180 cm) filled with water. Find the volume of water left in the larger cylinder after immersing the solid.
8️⃣ A spherical glass vessel has a cylindrical neck 8 cm long and 2 cm in diameter. The diameter of the spherical part is 8.5 cm. A child finds its volume to be 345 cm³. Check whether she is correct, assuming π = 3.14.