Mensuration Test - 4

Radius of tower = 5/2m
Height of tower = 14 m
∴ Curved surface area =2πrh =2 × 22/7 × 5/2 × 14 = 220m²
∴Cost of white washing the curved surface area = 220 × 50/100 = Rs.110

Thickness of the hollow metallic cylinder = 2 cm
Height of the cylinder = 70 cm
Let R and r be the outer and inner radii of the cylinder
∴R = 14cm and r − 14 − 2 = 12cm
Volume of the metal used = πh(R² − r²)
= 22/7 × 70(14²−12²) = 220 × 52 = 11440 
If the metal weighs 8g per cm³, so 11440cm³.
Metal weigh = 11440 × 8 = 91.520g

Thickness of wood = 1cm
Internal length of wooden box = 40−(1+1)=38cm
Internal breadth of the box =34−(1+1)−32 cm
Internal height of wooden box −30−(1+1)=28 cm
∴ Internal volume of box=(38×32×28)cm³
=34,048cm³
External volume of box=(40×34×30)cm³
=40,800cm³
∴ Volume of wood used
=External volume - Internal volume =40,800-34,048
=6752 cm³

Volume of rectangular block of ice =(40×25×15)cm³ = 15000cm³
Now, weight of 1cm³ of water =1gm Weight of 1 cm³ of ice =(9/10)^th of weight of 1cm³ of water
∴ Weight of 1cm³ of ice = (9/10)gm
∴ Weight of rectangular block of ice =(9/10×15000)gm
=13.5kg

Surface area of walls and ceiling =2h(l+b) + lb=2×4(9+6)+9×6 =120+54=174m²
Cost of plastering walls and ceiling =Rs. (174×2.5)=Rs. 435