Learn UNIT VI: Mensuration with Free Lessons & Tips

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.

To find the radius of the circle formed by bending a wire into an arc subtending an angle of 60∘, we can use the formula for the length of an arc of a circle:

To solve this problem, we first find the area the calf can graze with a rope of length 6 m and then find the area it can graze with a rope of length 11.5 m. The difference between these areas will give us the increase in the area of the grassy lawn the calf can graze.

The circumference of a circle is given by the formula:

To find the area of the shaded region, we need to subtract the area of the square OABC from the area of the quadrant OABQ.

To find the area of the shaded region, we need to subtract the area of the semi-circle from the area of the quadrant.

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.