The material of a cone is converted into the shape of a cylinder of equal radius . If the height of the cylinder is 5 cm. the height of the cone is?

Total volume of cuboid = (10 x 5 x 2) cm³
= 100 cm³
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm³
= 66 cm³
% of wood wasted = (100 - 66)% = 34 %

Number of balls = Volume of big ball / Volume of 1 small ball
= [4/3 x ? x 10 x 10 x 10] / [4/3 x ? x 0.5 x 0.5 x 0.5]
= 8000

Number of bullets = Volume of cube / Volume of 1 bullet
= (22 x 22 x 22)/(4/3 x 22/7 x 1 x 1 x 1)
= 2541.

Curved surface area = ?rl
= (22/7 x 6 x 28) cm²
= 528 cm²

Let their radii be x and 2x .
Ratio of their surface areas = [4?x²]/[4?(2x)²] = 1/4 = 1 : 4

? 1/3 ? x (2)² x h = ? x (2)² x 6
? h = 18 cm

Since the diameters are in the ratio 4 : 5. It follows that their radii are in the ratio 4 : 5.
Let them be 4r and 5r. Let the height be h and H .
? Ratio of volumes = [(1/3)?(4r)²h / (1/3)?(5r)²H
= (16h)/(25H)
? h/H = (1/4) x (25/16) = 25/64 = 25: 64.

? 1/3 x (22/7) x r² x 24 = 1232
? r² = 1232 x (7/22) x (3/24) = 49
? r = 7 cm
Now, h = 24
So, l = ?7² + (24)²
= ?625
= 25 cm
? Curved surface area = ?rl
= (22/7) x 7 x 25 cm²
= 550 cm²

Let h and H be the height of water level before and after the dropping of the sphere.
Then, [? x (30)² x H ] - [? x (30)² x h ]
= 4/3 ? x (30)³
? ? x 900 x (H -h) = 4/3 ? x 27000
? (H- h) = 40 cm

? 22/7 x r² = 154
? r² = 154 x (7/22) = 49
? r = 7 cm and h = 14
So, l = ?(7)² + (14)² = ?245 = 7?5 cm

? Area of curved surface = ?rl
= (22/7) x 7 x 7?5 cm²
= 154?5 cm²