Q. A juice-seller serves his customers using a glass whose inner diameter is 5 cm but the bottom of the glass has a raised hemispherical portion that reduces its capacity. If the height of the glass is 10 cm, find the apparent and actual capacities of the glass. [Use π = 3.14]
- Sol. Given, height of glass = 10 cm
- Diameter of glass = Diameter of the hemisphere
- = 5 cm
- Thus, radius of glass = Radius of the hemisphere
- = 2.5 cm
- Now, apparent capacity of the glass
- = π(2.5)2 10 cm^{3}
- = 196.25 cm^{3}
- And, actual capacity of the glass
- = Apparent capacity of the glass – Volume of the hemisphere
- =[196.25-(2/3)π(2.5)^{3}]cm^{3}
- = 163.54 cm^{3}
Q. A gulabjamun when ready for eating contains sugar syrup of about 30% of its volume. Find approximately how much syrup would be found in 45 such gulabjamuns if each of them is shaped like a cylinder with two hemispherical ends. The complete length of each of them is 5 cm and the diameter is 2.8 cm.[Use π =22/7]
Sol. Given, length of each gulabjamun = 5 cm
- diameter of each gulabjamun = 2.8 cm
- Thus, radius of each gulabjamun, r = 1.4 cm
- Total number of gulabjamuns = 45
- 3. Oxygen is used for respiration by both autotrophs and heterotrophs for oxidation of glucose to release chemical energy in the form of ATP.P ercentage of syrup in each gulabjamun = 30%
- and length of the cylindrical part
- = [5 – (1.4 + 1.4)] cm
- = (5 – 2.8) cm = 2.2 cm
Q. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.
- Ans. 2.5 m.
Q. A copper wire 3 mm in diameter is wound around a cylinder whose length is 12 m and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of the copper wire to be 8.88 g/cm.
- Ans. 12.57 m, 789.41 g.
Q. Selvi’s house has an overhead tank in the shape of a cylinder. It is filled up by pumping water from an underground tank that is cuboid in shape. The dimensions of the cuboid are 1.57 m × 1.44 m × 0.95 m. The radius of the overhead tank is 60 cm and its height is 95 cm. Find the height of the water-level in the underground tank after the overhead tank has been filled up completely. Compare the capacities of both the tanks. (Use π = 3.14)
- Ans. 47.5 cm, 1 : 2.
Q. Water in a canal, 6 m deep and 1.5 m wide is flowing at a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed for irrigation ?
- Ans. 562500 m^{2.}
Q. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 3 km/hr then in hw much time will the tank be completely filled ?
- Ans. 1 hour and 40 minutes.
Q. A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is 26 cm while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm while the diameter of the cylinder is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. [Use π = 3.14]
- Ans. 195.47 cm^{2.}
Q. A wooden toy was made from the rest of the solid cylinder after scooping out a hemisphere of same radius from each of it. If the height of the cylinder is 10 cm and its base radius is 3.5 cm, find the total surface area. [Use π =22/7]
- Ans. 374 cm^{2.}
Q. A tent is in the form of a right-circular cylinder of base diameter 4 m and height 2.1 m surmounted by a right circular cone of the same base radius and slant height 2.8 m. Find the area of the canvas used and the cost of canvas at ₹ 500 per square metre.
- Ans. ₹ 22000.
Q. A solid is in the shape of a cone mounted on a hemisphere, the radius of each of them being 1 cm and the total height of the cone equal to its radius. Find the volume of the solid in terms of π.
- Ans. π cm^{3.}