**Mensuration Exercise 15.5 – Questions**

**A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends. If the total length of the tank is 6m and the radius is 1m, what is the capacity of the tank in litres.****A rocket is in the shape of a cylinder with a cone attached to one end and a hemisphere attached to the other. All of them are of the same radius of 1.5m. The total length of the rocket is 7m and height of the cup is 2m. Find the volume of the rocket.****A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is 8cm and the total height of the cup is 11.5cm. Find the TSA of the cup.****A storage tank consists of a circular cylinder with a hemisphere adjoined on either ends. The external diameter of the cylinder is 1.4 m and length is 8m, find the cost of painting it on the outside at the rate of Rs. 10 per m**^{2}.**A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at 7 per Rs. 100 cm**^{2}.**A circus tent is cylindrical up-to a height of 3m and conical above it. If the diameter of the base is 105m and the slant height of the conical part is 53m, find the total cost of canvas used to make the tent if the cost of the canvas per m**^{2}is Rs. 100.

**Mensuration Exercise 15.5 – Solutions**

**A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends. If the total length of the tank is 6m and the radius is 1m, what is the capacity of the tank in litres.**

Solution:

r = 1m

total length of the tank = 6m

h = 6 – (1 + 1) = 6 – 2 = 4 m

Volume of the tank = volume of the hemisphere + volume of the cylinder + volume of the hemisphere

= ^{2}/_{3}πr^{3} + πr^{2}h + ^{2}/_{3}πr^{3}

= ^{2}/_{3} x ^{22}/_{7} x 1^{3} + ^{22}/_{7} x 1^{2} x 4 + ^{2}/_{3} x ^{22}/_{7} x 1^{3}

= 16.76 m

Capacity of the water tank in litres = 16.76 x 1000 = 16761.9 *l*

**A rocket is in the shape of a cylinder with a cone attached to one end and a hemisphere attached to the other. All of them are of the same radius of 1.5m. The total length of the rocket is 7m and height of the cup is 2m. Find the volume of the rocket.**

Solution:

r = 1.5 m

Height of the cylinder, h = 7 – (1.5 + 2) = 7 – 3.5 = 3.5 m

height of the cone = 2m

Volume of the rocket = Volume of the cone + volume of the cylinder + volume of hemisphere

= ^{1}/_{3}πr^{2}h+ πr^{2}h + ^{2}/_{3}πr^{3}

= ^{1}/_{3 }x ^{22}/_{7} x (1.5)^{2} x 2 + ^{22}/_{7} x (1.5)^{2 }x 3.5 + ^{2}/_{3 }x _{ }^{22}/_{7} x (1.5)^{3}

= 36.53 m^{3}

**A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is 8cm and the total height of the cup is 11.5cm. Find the TSA of the cup.**

Solution:

total height of the cup = 11.5 cm

Height of the cylindrical portion = 8 cm

Height of the hemisphere = 11.5 – 8 = 3.5 cm

r = 3.5 cm

TSA of the cup = TSA of cylinder + TSA of hemisphere

= 2πrh + 2πr^{2}

= 2 x ^{22}/_{7} x 3.5 x 8 + 2 x ^{22}/_{7} x 3.5^{2}

= 253 cm^{2}

** **

**A storage tank consists of a circular cylinder with a hemisphere adjoined on either ends. The external diameter of the cylinder is 1.4 m and length is 8m, find the cost of painting it on the outside at the rate of Rs. 10 per m**^{2}.

Solution:

External diameter = 1.4 m

Radius = ^{d}/_{2} = ^{1.4}/_{2} = 0.7 m

length = 8m

length of the hemisphere = 8 – (0.7+0.7) = 6.6 m

Total surface area of the storage tank = TSA of the cylindrical part + 2x TSA of hemispherical part

= 2πr(r +h) + 2 x 3 πr^{2}

= 2x^{22}/_{7}x(0.7)(0.7+6.6)+2x3x^{22}/_{7} x (0.7)^{2}

= 41.36 m^{2}

Cost of polishing at the rate of Rs. 10 per m^{2} = 41.34 x 10 = Rs. 413.6

**A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at 7 per Rs. 100 cm**^{2}.

Solution:

diameter of the base of the cone = 16 cm

radius of the base of the cone = 8 cm

height = 15 cm

l^{2} = r^{2} + h^{2}

= 8^{2} + 15^{2}

= 64 + 25

= 289

l = 17 cm

Surface area of the toy = CSA of hemisphere + CSA of cone

= 2πr^{2} + πrl

= 2 x ^{22}/_{7} x 8^{2} + ^{22}/_{7} x 8 x 17

= 829.71 cm^{2}

Cost of painting the toy at Rs. 7 per 100 cm^{2} = ^{829.71×7}/_{100} = Rs. 58.08

**A circus tent is cylindrical up-to a height of 3m and conical above it. If the diameter of the base is 105m and the slant height of the conical part is 53m, find the total cost of canvas used to make the tent if the cost of the canvas per m**^{2}is Rs. 100.

Solution:

d = 105 m

r = ^{d}/_{2} = ^{105}/_{2} = 52.5 m

h = 3m

l = 53 m

l^{2 }= r^{2} + h^{2}

53^{2} = 52.5^{2} + h^{2}

53^{2} – 52.5^{2} = h^{2}

52.75 = h^{2}

h = 7.26 m

Total canvas used = CSA of cylindrical part + CSA of conical part

= 2πrh + πrl

= 2 x ^{22}/_{7} x 52.5 x 3 + ^{22}/_{7} x 52.5 x 53

= 9735 m^{2}

The total cost of canvas used to make the tent if the cost of the canvas per m^{2} is Rs. 100 = 9735 x 100 = Rs. 97,35,000