Mensuration Quiz

A sector with a central angle 120° and a radius of 21 cm was made into a cone. Find the height of the cone.

1. 16.8 cm
2. 20.5 cm
3. 24.56 cm
4. 19.8 cm

Answer: (d) 19.8 cm

A recycling plant processes 60,000 aluminium cans, each containing 6 cm³ of aluminium. During the process, 12% of the metal is lost. How many cubic metres of aluminium remain after melting?

1. 0.3168 m3
2. 316800 m3
3. 3165800 m3
4. 360000 m3

Answer: (a) 0.3168 m3

A square whose side is 2 m has its corners cut away to form an octagon with all sides equal. Then, what is the value side of the octagon?

1. √ 2/(1 - √ 2) m
2. √2/(1 + √ 2) m
3. (1 + √ 2)/2 m
4. (1 - √ 2)/2 m

Answer: (b) √2/(1 + √ 2) m

The volume of a cuboid is 15360 cm3 and its length is 20cm. The ratio of its breadth to height is 4 : 3. The sum of the breadth and height is 56 cm, find the total surface area of the cuboid.

1. 3062 cm2
2. 2196 cm2
3. 3776 cm2
4. 1888 cm2

Answer: (c) 3776 cm2

The sum of the length, breadth and height of a cuboid is 36 cm. The length of its diagonal is √350 cm. Calculate the total surface area of the cuboid.

1. 542 cm2
2. 412 cm2
3. 946 cm2
4. 350 cm2

Answer: (c) 946 cm2

The length, breadth and height of a cuboid are in the ratio 2 : 3 : 4. If the length, breadth, and height of the cuboid are increased by 50%, 75%, and 100% respectively. Find the increase in the volume of the cuboid if the real volume is 24000 m3.

1. 150000 m3
2. 10000 m3
3. 204000 m3
4. 102000 m3

Answer: (d) 102000 m3

Read the following passage and answer the following question: In the development of a new public park, planners decide to incorporate a distinctive hexagonal pavilion as a centerpiece. The pavilion has a regular hexagonal base with each side measuring 10 m. Above the base, there is a slanted roof that peaks at a central point 5 m above the base, resembling a pyramid with a hexagonal base.The roof is designed using triangular panels, each corresponding to one of the hexagon's sides. These panels are tilted at an angle to channel rainwater towards the exterior of the pavilion. The park's designers need to calculate various areas to accurately order materials and plan the construction process. Calculate the increase in the total roof area if the height of the pavilion is increased by 2 m while keeping the base dimensions the same. Use the original slant height for calculations.

1. 45.9 m2
2. 27.9 m2
3. 43 m2
4. 258 m2

Answer: (a) 45.9 m2

The radii of the bases as well as the heights of a cone and a cylinder are each equal to h and the radius of a hemisphere is also equal to h. Find the ratio of the volume of cylinder, hemisphere and cone.

1. 4 : 3 : 2
2. 2 : 3 : 4
3. 1 : 2 : 3
4. 3 : 2 : 1

Answer: (d) 3 : 2 : 1

Twenty-five cylindrical cans, each with a radius of 1.5 units, are placed inside a cardboard box, arranged 5 in a row. If the cans touch adjacent cans and the walls of the box, what is the remaining area of the bottom of the box in square units?

1. 40.25 units2
2. 48.25 units2
3. 225 units2
4. 176.75 units2

Answer: (b) 48.25 units2

The angle subtended by an arc at the centre of a circle is 60°. If the circumference of the circle is 132 cm, and its radius is utilized to cut a metal sheet that surrounds the sector with a border 4 cm wide, Calculate the total area of the metal sheet used, including the border.

1. 327.08 cm2
2. 625.08 cm2
3. 230.79 cm2
4. 414.09 cm2

Answer: (a) 327.08 cm2