Mensuration Questions
Study the volume and surface-area formulas for hemispheres and cylinders. Practise questions involving dimensions, equal volumes, and converting one solid into another to strengthen your mensuration skills.
26 questions
- An architect is designing a right prism-shaped skylight with a rectangular base measuring 9 cm by 12 cm and a height of 16 cm. Determine the length of the longest…
- A circular park has a radius of 8 cm, and a special garden area is designed as a sector with an area of 32π cm². Find the length of the…
- In a square pyramid, the base side is 6 cm and slant height is 10 cm. Find lateral surface area.
- Find the area of a quarter-circle with radius 7 cm.
- A plane parallel to the base of a pyramid cuts it at half its vertical height from the apex. What is the ratio of the volume of the smaller pyramid…
- A hemispherical water tank has an internal radius of 21 m. It is full of water and is being emptied by a pump at a rate of 100 litres per…
- A brine tank has 100 liters of 40% salt solution. Water is added to reduce it to 25%, but then 10 liters are lost due to overflow. What was the…
- An architect is designing a square-based pyramid for a public monument. The base has a perimeter of 60 m, and the total lateral surface area (the sum of the four…
- A prism has a base of area 35 cm² and height 6.5 cm. What is the volume?
- The diagonal of the square base of a right square pyramid is 10√2 cm. If the lateral surface area of the pyramid is 260 cm², calculate the volume of the…
- The ratio of the volumes of two hemispheres is 27: 64. What is the ratio of their total surface areas?
- A square tile has area 72 cm². What is the length of each side in simplest surd form?
- A square pyramid has a base side of 6 cm and height 9 cm. Find the volume.
- A rectangular prism has volume 288 cm³ and base dimensions 6 cm and 4 cm. Find its height.
- If a circular wire is bent to form a square, and the radius of the circle is 14 cm, what is the side of the square?
- The total surface area of a hemisphere is 462 cm². What is its curved surface area? (Use \(\pi=\frac{22}{7}\))
- The ratio of the curved surface area of a cylinder to its total surface area is 7:10. If the volume of the cylinder is 12672 cm³, find its curved surface…
- A farmer wants to fence a triangular field with sides 60 m, 111 m, and 123 m. If the cost of fencing is ₹18 per meter, what will be the…
- A rectangular tile having a perimeter of 224 cm has been used to pave a floor of length and breadth 25.6 m and 14.4 m, respectively. If the ratio of…
- The length and breadth of a rectangle are in the ratio 14:11, respectively, and the perimeter of the rectangle is 150 cm. If the area of the rectangle is equal…
- A hemispherical tank has an inner radius of 3 m. It is filled with water at a rate of 1800π liters per minute. How long will it take to fill…
- A solid metal sphere with a radius of 12 cm is melted and transformed into multiple smaller spheres, each with a radius of 2 cm. How many smaller spheres can…
- The numerical value of the volume of a hemisphere is equal to the numerical value of its total surface area. What is the radius of this hemisphere in units?
- A solid right circular cylinder is melted down and recast into a right circular cone with the same base radius. If the cylinder's height is h, what is the height…
- A solid hemispherical block is melted and recast into a cylinder of the same radius. The height of the cylinder is what fraction of the radius of the hemisphere?