Advertisements
Advertisements
Question
A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
Solution
Given,
The outer and inner diameters of pipe are 8 cm and 7 cm.
Dimensions of a solid cuboid of iron = 53 cm × 40 cm × 15 cm.
When a shape melted and recast into another shape volume will remain same.
Volume of cubical iron = volume of cylindrical pipe
length × breadth × height = π(R2 − r2)h
53 × 40 × 15 = `22/7 xx (4^2 - (7/2)^2)h`
53 × 40 × 15 = `22/7 xx 15/4 xx h`
h = `(53 xx 40 xx 15 xx 7 xx 4)/(22 xx 15)`
h = 2698.18 cm = 27 m [∵ 1 m = 100 cm]
APPEARS IN
RELATED QUESTIONS
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
1) The area of the metal sheet used to make the bucket.
2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
A plumbline (sahul) is a combination of
Match the following columns:
| Column I | Column II |
| (a) The radii of the circular ends of a bucket, in the form of the frustum of a cone of height 30 cm, are 20 cm and 10 cm respectively. The capacity of the bucket is ........cm3. |
(p) 2418π |
| (b) The radii of the circular ends of a conical bucket of height 15 cm are 20 and 12 cm respectively. The slant height of the bucket is ........ cm. |
(q) 22000 |
| (c) The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is .........cm2. |
(r) 12 |
| (d) Three solid metallic spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ........ cm. |
(s) 17 |
Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
The total surface area of a solid hemisphere of radius 7 cm is ______.
