Exercise 10.4

1. The radius of a sphere is 3.5 cm. Find its surface area and volume.

Solution:

Radius (r) = cm

Surface Area = 4πr^2 = 4 × (22/7) × (3.5)^2 = 4 × (22/7) × 12.25 = cm^2

Volume = (4/3)πr^3 = (4/3) × (22/7) × (3.5)^3 = (4/3) × (22/7) × 42.875 ≈ cm^3

2. The surface area of a sphere is 1018 2/7 sq.cm. What is its volume?

Solution:

Surface Area = 1018 27 = 7130720367 cm^2

4πr2πr2 = 7130/7

r2 = (7130/7) × (7/8888/7) ≈

r ≈ √92.33 ≈ 9.618.51 cm

Volume = (4/3)πr3 ≈ (4/3) × (22/7) × 9.613 ≈ cm^3

3. The length of equator of the globe is 44 cm. Find its surface area.

Solution:

Circumference (2πr) = cm

2πr = 44

r = 44 × (744447) = cm

Surface Area = 4πr2 = 4 × (22/7) × 72 = cm^2

4. The diameter of a spherical ball is 21 cm. How much leather is required to prepare 5 such balls.

Solution:

Diameter (d) = cm, Radius (r) = cm

Surface Area of one ball = 4πr2 = 4 × (22/7) × 10.52 = cm^2

Leather for 5 balls = 1386 × 5 = cm^2

5. The ratio of radii of two spheres is 2: 3. Find the ratio of their surface areas and volumes.

Solution:

Radii: 2x,

Ratio of Surface Areas = (4π2x2)/(4π3x2) = 4:99:4

Ratio of Volumes = ((4/3)π2x3)/((4/3)π3x3) = 8:278:18

6. Find the total surface area of a hemisphere of radius 10 cm. (use π = 3.14)

Solution:

Radius (r) = cm

Total Surface Area = 3πr2 = 3 × 3.14 × 102 = cm^2

7. The diameter of a spherical balloon increases from 14 cm. to 28 cm. as air is being pumped into it. Find the ratio of surface areas of the balloons in the two cases.

Solution:

Initial Radius (r1) = 7 cm, Final Radius (r2) = 14 cm

Ratio of Surface Areas = (4π72)/(4π142) =

8. A hemispherical bowl is made of brass, 0.25 cm. thickness. The inner radius of the bowl is 5 cm. Find the ratio of outer surface area to inner surface area.

Solution:

Inner Radius (r) = 5 cm, Outer Radius (R) = 5.25 cm

Inner Surface Area = 2π52 = 50π

Outer Surface Area = 2π5.252 = 55.125π

Ratio = 55.125π / 50π =

9. The diameter of a lead ball is 2.1 cm. The density of the lead used is 11.34 g/cm^3. What is the weight of the ball?

Solution:

Radius (r) = 1.05 cm, Density = 11.34 g/cm^3

Volume = (4/3)π(1.05)^3 ≈ 4.851 cm^3

Weight = Volume × Density ≈ 4.851 × 11.34 ≈ g

10. A metallic cylinder of diameter 5 cm. and height 3 1/3 cm. is melted and cast into a sphere. What is its diameter.

Solution:

Cylinder Radius (r) = 2.5 cm, Cylinder Height (h) = 10/3 cm

Cylinder Volume = π(2.5)^2(10/3) = 62.5π/3

Sphere Volume = (4/3)πR^3 = 62.5π/3

R^3 = 15.625, R = 2.5 cm

Sphere Diameter = 2R = cm

11. How many litres of milk can a hemispherical bowl of diameter 10.5 cm. hold?

Solution:

Radius (r) = 5.25 cm

Bowl Volume = (2/3)π(5.25)^3 ≈ 303.1875 cm^3

Volume in litres ≈ 303.1875 ml = litres

12. A hemispherical bowl has diameter 9 cm. The liquid is poured into cylindrical bottles of diameter 3 cm. and height 3 cm. If a full bowl of liquid is filled in the bottles, find how many bottles are required.

Solution:

Bowl Radius (R) = cm, Bottle Radius (r) = cm, Bottle Height (h) = cm

Bowl Volume = (2/3)π(4.5)^3 = π

Bottle Volume = π(1.5)^2(3) = π

Number of Bottles =