CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends as 8cm and 20cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8per100cm2.


Open in App
Solution

It is given that,

R=20cmr=8cmh=16cm

Step 1 - Finding the cost of milk that it can contain.

Volumeoffrustum=13πhR2+r2+RrVolumeoffrustum=13×3.14×16202+82+20×8Volumeoffrustum=13×3.14×16624Volumeoffrustum=10449.92cm3

We know that 1cm3=1ml

10449.92cm3=1×10499.92=10499.92ml

We also know that, 1000ml=1litre

Therefore, 10449.92ml=10499.921000litre=10.49992litre

Costof1litremilk=20SoCostof10499.92litremilk=20×10499.92=208.998

Hence, the cost of milk in the container is 208.992.

Step 2 - Finding the cost of the metal sheet required to make the container.

Since, the container is open from the top.

So, the surface area of the container = Curved surface area of container + Area of the base of the container

We know the relation between the slant height, radii and height of the frustum is

l2=h2+R-r2l2=162+20-82l2=256+144l=400l=20cm

Now,

Surfaceareaofthecontainer=Curvedsurfaceareaoffrustum+AreaofthebaseoffrustumSurfaceareaofthecontainer=πR+rl+πR2Surfaceareaofthecontainer=πR+rl+R2Takingthevalueofπ=3.14Surfaceareaofthecontainer=3.1420+820+82Surfaceareaofthecontainer=1959.36cm2

Now, the metal sheet used to make the container is 1959.36cm2.

The cost of 100cm2 of the sheet = 8

The cost of 1959.36cm2 of the sheet = 8×1959.36100=156.748

Therefore, the cost of the metal sheet used to make the container is 156.748.

Hence, the cost of milk in the container is 208.992 and the cost of the metal sheet used to make the container is 156.748.


flag
Suggest Corrections
thumbs-up
1
BNAT
mid-banner-image
similar_icon
Similar questions
View More