Learn UNIT VI: Mensuration with Free Lessons & Tips

To find the volume of the iron required to construct the open box, we first need to calculate the volume of the outer box and then subtract the volume of the inner box (with thickness) from it.

To find the length of the wire formed by the frustum of the cone, we'll first calculate the dimensions of the frustum.

To find the volume of water left in the cylinder after placing the cone inside, we need to consider the volumes of both the cone and the cylinder. 

To find the volume of the wood in the entire pen stand, we need to calculate the volume of the cuboid and the volumes of the four conical depressions and the cubical depression, and then subtract these volumes from the volume of the cuboid.

To find the volume of the remaining solid after hollowing out a conical cavity from a cube, we'll calculate the volumes of the cube and the conical cavity, and then subtract the volume of the conical cavity from the volume of the cube.

When a solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base, the resulting smaller cone is similar to the original cone but with half the height.

Let's denote:

• rr as the radius of the base of the cylinder,
• hh as the height of the cylinder.

Given:

To find the area of the minor segment of a circle, we first need to find the area of the corresponding sector and then subtract the area of the corresponding triangle from it.

Let's denote:

• C as the circumference of the circle,
• r as the radius of the circle.

Given:

To solve this problem, we first need to find the areas of the two circles with diameters 10 cm and 24 cm. Then, we'll add these areas together to find the total area. Finally, we'll find the diameter of the larger circle whose area is equal to the sum of the areas of the two smaller circles.