Mensuration quiz

The area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm is:

The area of a rhombus whose diagonals are 10 cm and 8 cm is:

The volume of a cube of edge 5 cm is:

The total surface area of a cube of edge 4 cm is:

1 m^3 is equal to:

The curved surface area of a cylinder of radius r and height h is:

The lateral surface area of a cuboid of length l, breadth b and height h is:

The volume of a cuboid measuring 10 cm by 5 cm by 4 cm is:

If the radius of a cylinder is doubled and its height is unchanged, its volume becomes:

A cuboidal box in which every edge is 6 cm long is:

A field is in the shape of a trapezium whose parallel sides are 15 m and 25 m and the distance between them is 10 m. Find its area. (2 marks)

Find the area of a rhombus whose diagonals are 16 cm and 12 cm. Also find the length of its side. (2 marks)

The base area of a cuboid is 180 cm^2 and its volume is 900 cm^3. Find its height. (2 marks)

Find the volume of a cylinder of radius 7 cm and height 10 cm in cm^3 and in litres. (2 marks)

How many cubes of edge 1 cm can be packed in a cube of edge 5 cm? (2 marks)

Explain the difference between surface area and volume, giving one situation in which each is needed. (2 marks)

The volume of a cube is 512 cm^3. Find the length of its edge. (2 marks)

A room is 5 m long, 4 m wide and 3 m high. Find the area of its four walls. (2 marks)

A cylindrical pillar has diameter 50 cm and height 3.5 m. Find the cost of painting its curved surface at Rs 12.50 per m^2. (2 marks)

A milk tank is in the form of a cylinder of radius 1.5 m and length 7 m. Find the quantity of milk in litres that it can hold. (2 marks)

A diagonal of a quadrilateral is 24 cm, and the perpendiculars dropped on it from the remaining two vertices are 8 cm and 13 cm. Find the area of the quadrilateral. (3 marks)

A cuboidal tank is 2 m long, 1.5 m wide and 1 m deep. Find its capacity in litres. How long will it take to fill it with a pipe that delivers 50 litres per minute? (3 marks)

The volume of a cylinder is 448 pi cm^3 and its height is 7 cm. Find its radius. (3 marks)

A cubical box has edge 10 cm and a cuboidal box measures 12.5 cm by 10 cm by 8 cm. Which box has the greater lateral surface area and by how much? Which has the greater total surface area and by how much? (3 marks)

A hall measures 15 m by 8 m by 6 m. Find its volume. If each person needs 4 m^3 of air, how many persons can the hall hold? (3 marks)

Read the passage and answer the questions. A town park is in the shape of a trapezium whose parallel sides are 50 m and 30 m, and the distance between them is 20 m. Inside the park there is a flower bed shaped like a rhombus with diagonals 8 m and 6 m; the rest of the park is to be covered with grass. (i) Find the area of the park. (ii) Find the area to be covered with grass. (iii) Find the cost of planting grass at Rs 15 per m^2. (5 marks)

Read the passage and answer the questions. A road roller is a cylinder of diameter 84 cm and length 1 m. It takes 750 complete revolutions to level a playground once. (i) Find the curved surface area of the roller in m^2. (ii) Find the area of the playground. (iii) Find the cost of levelling the playground at Rs 2 per m^2. (5 marks)

Read the passage and answer the questions. A juice company sells juice in cuboidal packs measuring 8 cm by 5 cm by 12.5 cm. Each pack is made of cardboard and is completely filled. (i) Find the volume of juice in one pack in cm^3 and in litres. (ii) How many packs can be filled from 1000 litres of juice? (iii) How much cardboard is needed to make one pack? (5 marks)

Read the passage and answer the questions. A village has a cylindrical overhead water tank of radius 3.5 m and height 10 m. The village has 700 people, and each person uses about 50 litres of water a day. (i) Find the capacity of the tank in litres. (ii) For how many full days will a full tank meet the needs of the village? (iii) Find the area of the curved surface to be painted on the outside of the tank. (5 marks)

Read the passage and answer the questions. A classroom is 10 m long, 8 m wide and 4 m high. It has one door 2 m by 1 m and two windows, each 1.5 m by 1 m. The walls and the ceiling are to be painted. (i) Find the area of the four walls. (ii) Find the area of the walls to be painted after leaving out the door and the windows. (iii) Find the total cost of painting the walls and the ceiling at Rs 20 per m^2. (5 marks)

Draw a trapezium and show how it can be divided into two triangles to derive the formula for its area. Use the formula to find (i) the area of a trapezium with parallel sides 20 cm and 12 cm and height 9 cm (ii) the height of a trapezium whose area is 180 cm^2 and whose parallel sides are 25 cm and 15 cm. (6 marks)

In a surveyor's field book, the diagonal AD of a field ABCDE is 20 m. B and C lie on one side of AD: the perpendicular from B meets AD 4 m from A and is 6 m long, and the perpendicular from C meets AD 14 m from A and is 8 m long. On the other side of AD, the perpendicular from E is 10 m long. Draw a rough sketch of the field, divide it into triangles and a trapezium, and find its total area. (6 marks)

Draw the net of a cuboid and use it to derive the formula for its total surface area. A hall is 15 m long, 10 m wide and 7 m high. Its four walls and ceiling are to be painted, and one can of paint covers 100 m^2. How many cans are needed? (6 marks)

Draw a closed cylinder and its net, and use it to explain the formulas for its curved and total surface areas. A closed cylindrical petrol tank has diameter 4.2 m and height 4.5 m. Find the area of steel used to make it. If 1/12 of the steel actually used was wasted in making the tank, find the total steel used. (6 marks)

Rain water falling on a flat rectangular roof 22 m by 20 m drains into a cylindrical vessel of diameter 2 m and height 3.5 m. Draw a labelled sketch of the roof and the vessel. If the vessel is just full after a shower, find the volume of water collected and the height of rainfall in cm. (6 marks)