Let h be the height,
Volume of the cone = V
and curved surface area of the cone = c
? 1/3 ?r²h = V, ?rl = c
i.e., ?r?r² + h² = c
?²r²(r² + h²) = c²
Consider 3?Vh³ - c²h² + 9V²
= 3? x 1/3?r²h x h³ - ?²r²(r² + h²)h + 9 x 1/9 x ?²r⁴ h²
= ?²r²h⁴ - ?²r⁴h² - ?²r²h⁴ + ?²r⁴ = 0

Let the side of the cube be 3k, 4k and 5k, respectively.
So, volumes of these cubes are 27 k³, 64k³, 125 k³ respectively.
? Volume of the new bigger cube = 27 k³ + 64k³ + 125 k³
= 216k³
So, side of the new cube = 6k
Since, diagonal of the cube = ?(6k)² + (6k)² + (6k)²
= 12?3
? 108k² = 432
?k = 2
So, sides of the three cubes were 6 cm, 8 cm and 10 cm respectively.

External radius = 2.5 cm,
length = 100 cm
? External volume = [? x (2.25)² x 100] cm²
internal radius = 1.5 cm
? internal volume = [? x (1.5)² x 100]cm³
Volume of metal
= [? x (2.5)² x 100 - ? x (1.5)² x 100] cm³
= ? x 100 x [(2.5)² - (1.5)²] cm³
= (22/7 x 100 x 4 x 1 x 21/1000) kg
= 26.4 kg.

Curved surface area of cylinder = 2?rh cm²
Total surface area of cylinder = 2?r(h + r) cm²
Now, According to the question
2?rh/2?r(h + r) = 1/2
? h/(h + r) = 1/2
? 2h = h + r
? Now, Total surface area = 616 cm²
? 2? (h + r) = 616
? 2?r (r + r) = 616 (? h = r)
? 2?r(2r) = 616
? 4?r² = 616
? r = ?style="text-decoration:overline">616/4?
= ?616 x 7/4 x 22
= ?7 x 7 =
? r = h = 7 cm
? Volume = ? r² h
= (22/7) x (7 x 7) x 7 = 1078 cm³

If 10 circular plates each of thickness 3 cm, each are placed one above the other, then it forms a cylinder with height (3 x 10 = 30 cm) and a hemisphere of radius 6 cm is placed on the top just to cover the cylinder that means its radius is 6 cm also
? Radius of hemisphere (R) = 6 cm
Radius of cylinder (r) = 6 cm
and height of cylinder (h) = 30 cm
? Volume of the solid = Volume of cylinder + Volume of hemisphere
= ?r²h + (2/3)?R³
= ?(6)² x 30 + (2/3)?(6)³
= ? x 36 x 30 + (2/3)? x 216
= 1080? + 2? x 72 = 1080? + 144?
= 1224? cm³
Which is the required volume of solid.

Area of the square = 1 2 × d i a g o n a l 2=  1/2 * 3.8 * 3.8 = 7.22 sq.m

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. 

Area of each tile = (41 x 41) sq.cm 

Required number of tiles = 1517 x (902/41) x 41 = 814

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter = 5300 m = 200 m. 26.50

2[(x + 20) + x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length = x + 20 = 60 m.

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter = 5300 m = 200 m. 26.50

2[(x + 20) + x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length = x + 20 = 60 m.