Question

1) A toy is in the form of a cylinder of diameter 2root2 m and height 3.5 m surmounted by a cone whose vertical angle is 60degree .Find total surface area and volume of the toy.

2)three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose edges is 12cm Find the edge of the three cubes.

Answer 1

1)

SEE THE ATTACHED IMAGE

Angle FAC = 30

In triangle FAC

Sin A = CF/AC  = √2/AC

AC = 2√2
Cos 30 = AF/AC

√3/2 x 2√2 = AF

AF = √6
Surface area = 2(pi)rh + (pi)rl + (pi)r²

= 2(3.14)(√2)(3.5) + 3.15(2)(√2)² + 3.15(√2)²

= 44.67 m²
Volume = 1/3(pi)r^2h + )pi)r²H

= (pi)r²(1/3h + H)

= 3.14(√2)^2(1/3 x√6 + 1.3)

= 13.29 m³



2)
Take the dimensions of the cubes to be 3x, 4x and 5x respectively

Total volume of the small cubes = volume of the big cube

(3x)³ + (4x)³ + (5x)³ = 12³

27x³ + 64x³ + 125x³= 1728

216x³ = 1728

x³ = 8

x = 2

So, the edge of the small cubes = 3(2), 4(2) and 5(2)

                                                    = 6 cm by 8 cm by 10 cm