Question

Playing in a ball pool is good entertainment for kids. Suhana bought 600 new balls of diameter 7 cm to fill in the pool for her kids. The cuboidal box containing 600 balls has dimensions 42 cm × 91 cm × 50 cm (l × b × h).

Based on the above information, answer the following questions.

1. Find the volume of one ball.  (1)
2. 10 balls are painted with neon colours. Determine the area of painted surface.  (1)
3. 1. Find the volume of empty space in the box.   (2)
      OR
   2. The lowermost layer of the balls covers the base of the box, edge to edge, when the balls are placed evenly adjacent to each other.  (2)
      1. How much area is covered by one ball?
      2. How many balls are there in the lowermost layer?

Answer 1

i. Radius of one ball = `7/2` cm

Volume of one ball = `4/3 πr^3`

= `4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2`

= 179.67 cm³

ii. Area of one ball = 4πr²

= `4 xx 22/7 xx 7/2 xx 7/2`

= 154 cm²

Now, Area of 10 balls = 154 × 10

= 1540 cm²

Thus, the area of pointed surface is 1540 cm².

iii. a. Volume of box = 1 × b × h

= 42 × 91 × 50

= 191100 cm³

Total volume of 600 balls = 600 × 179.67

= 107802 cm² 

Now, Volume of empty box = Volume of box – Total volume of 600 balls

= 191100 – 107802

= 83298 cm³

OR

b. A. Since each ball covers a circular area.

Then, area covered by one ball = πr²

= `22/7 xx 7/2 xx 7/2`

= `77/2`

= 38.5 cm²

B. The base of the box has dimensions 42 cm × 91 cm.

Then, base area = 42 × 91

= 3822 cm² 

Number of balls = `"Base area"/"Area of one ball"`

= `3822/38.5`

= 99.27

≈ 99

Hence, 99 balls are there in the lowermost layer.