SSC GD (MENSURATION)

A solid metallic cube of side $9 \mathrm{~cm}$ and solid metallic cuboid having dimensions $5 \mathrm{~cm} \times 13 \mathrm{~cm} \times 31 \mathrm{~cm}$ are melted to form a single cube. How much (in ₹) is the cost to polish the new cube at a rate of ₹ 10 per $\mathrm{cm}^2$ ?

A square has a bounding of 16 cm. From each of the four corners of this square, a small square of 1 cm is cut off. What will be the length of the boundary of the remaining figure?

The angles of rotations (rotational symmetry) of an equilateral triangle are:

The curved surface area of a right circular cylinder is $1320 \mathrm{~cm}^{2}$ and the radius of its base is $10.5 \mathrm{~cm}$. The volume (in $\mathrm{cm}^{3}$ ) of the cylinder is: (Take $\pi=\frac{22}{7}$ )

The area of a triangular park, whose sides are $72 \mathrm{~m}, 210 \mathrm{~m}$ and $222 \mathrm{~m}$, is equal to the area of a rectangular garden whose sides are in the ratio of $21: 10$. What is the perimeter (in $\mathrm{m}$ ) of the rectangular garden?

When a rectangular sheet folded into two equal halves, a rectangular sheet had a perimeter of $36 \mathrm{~cm}$ for each part folded along one set of sides, and the same is $45 \mathrm{~cm}$ when folded along the other set of sides. The area (in $\mathrm{cm}^{2}$ ) of the sheet is:

The width of the path around a square field is $4.5 \mathrm{~m}$ and its area is $105.75 \mathrm{~m}^{2}$. Find the cost of fencing the square field at the rate of ₹100 per metre.

The length and breadth of a rectangle are increased by $8\%$ and decreased by $10\%$ respectively. Calculate the percentage increase or decrease in its area.

The area (in m$^2$) of a triangular field, whose sides are 85 m, 85 m and 154 m, is:

If the volume of a cube is $192 \sqrt{3}$ cubic cm, then the length of its diagonal is: