**Exercise 21.1**

**Question 1: Find the surface area of a sphere of radius:**

**(i) 10.5 cm (ii) 5.6 cm (iii) 14 cm**

**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

**Question 2: Find the surface area of a sphere of diameter:**

**(i) 14 cm (ii) 21 cm (iii) 3.5 cm**

**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

**Question 3: Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm. (π = 3.14)**

**Solution:**

^{2}

^{2 }

^{2}

^{2}

^{2}

^{2}

**Question 4: The surface area of a sphere is 5544 cm**

^{2}, find its diameter.**Solution:**

^{2}

^{2}

^{2}= 5544

^{2}= (5544 × 7)/(22 × 4)

^{2}= (5544 × 7)/88

^{2}= (5544 × 7)/88

^{2}= 63×7

^{2}= 441

**Question 5: A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin plating it on the inside at the rate of Rs.4 per 100 cm**

^{2}.**Solution:**

^{2}

^{2}

^{2}

^{2}area is Rs.4

^{2}area = Rs. 4 × 173.25/100 = Rs. 6.93

**Question 6: The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq m.**

**Solution:**

^{2}

^{2}

^{2}

^{2}= Rs.2

^{2}

**Exercise 21.2**

**Question 1: Find the volume of a sphere whose radius is:**

**(i) 2 cm (ii) 3.5 cm (iii) 10.5 cm.**

**Solution:**

^{3}

^{3}

^{3 }

^{3}

^{3}

^{3 }

^{3}

^{3}

**Question 2: Find the volume of a sphere whose diameter is:**

**(i) 14 cm (ii) 3.5 dm (iii) 2.1 m**

**Solution:**

^{3 }

^{3}

^{3}

^{3}

^{3}

^{3}

^{3}

^{3}

^{3}

**Question 3: A hemispherical tank has the inner radius of 2.8 m. Find its capacity in litre.**

**Solution:**

^{3}

^{3 }

^{3}

^{3}= 1000 litres

**Question 4: A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. Find the volume of steel used in making the bowl.**

**Solution:**

^{3}- 2/3 πr

^{3 }

^{3}- r

^{3})

^{3}− (5)

^{3})

^{3}

^{3}

**Question 5: How many bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 cm in diameter?**

**Solution:**

^{3 }

^{3 }

^{3}

^{3}

^{3}

^{3}

**Question 6: A shopkeeper has one laddoo of radius 5 cm. With the same material, how many laddoos of radius 2.5 cm can be made?**

**Solution:**

^{3}

^{3}

^{3}

^{3}

^{3 }

^{3}

**Question 7: A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be 3/2cm and 2 cm, find the diameter of the third ball.**

**Solution:**

^{3}

^{3}

**Question 8: A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises 5/3cm. Find the radius of the cylinder.**

**Solution:**

^{3}

^{3}

^{2}h

^{2}h = 4/3πr

^{3}

^{2}× 5/3 = 4/3 × π × 125

^{2}= 4/3 × 125 × 3/5

^{2}= 4 × 25

^{2}= 100

**Question 9: If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?**

**Solution:**

^{3}

**Question 10: A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.**

**Solution:**

^{2}h = 2/3 πr

^{3}

^{2}h = 2r

^{3}

^{3})/r

^{2}

**Question 11: A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.**

**Solution:**

^{3}= π(R)

^{2}h

^{3}= π(7)

^{2}h

**Question 12: A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.**

**Solution:**

^{2}h = 4/3πR

^{3}

^{2}× (4r/3) = 4/3 π (4)

^{3}

^{2}× (r) = (4)

^{3}

^{3}= (4)

^{3}

^{3}= 4×4×4

**Question 13: A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.**

**Solution:**

_{1}) = 6cm

_{2}) = 4cm

^{3}= πr

^{2}h

^{3}= π × (4)

^{2}× h

**Question 14: A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?**

**Solution:**

^{3}= πR

^{2}h

^{3}= π × (16)

^{2}× 9

^{3}= 16 × 16 × 9

^{3}= (16 × 16 × 9 × 3)/4

^{3}= 16 × 4 × 9 × 3

^{3}= 1728

**Exercise VSAQs ..........................**

**Question 1: Find the surface area of a sphere of radius 14 cm.**

**Solution:**

^{2}

^{2}

**Question 2: Find the total surface area of a hemisphere of radius 10 cm.**

**Solution:**

^{2}

^{2}

**Question 3: Find the radius of a sphere whose surface area is 154 cm**

^{2}.**Solution:**

^{2}

^{2}

^{2}= 154

^{2}= 154

^{2}= (154 × 7)/(22 × 4)

^{2}= (7 × 7)/4

^{2}= 49/4

^{2}= √(49/4)

**Question 4: The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.**

**Solution:**

^{2}

^{2}

^{2}.

**Question 5: Find the volume of a sphere whose surface area is 154 cm**

^{2}.**Solution:**

^{2}

^{2}

^{2}= 154

^{2}= 154

^{2}= (154 × 7)/(22 × 4)

^{2}= (7 × 7)/4

^{2}= 49/4

^{2}= √(49/4)

^{3}

^{3}.