Advertisements
Advertisements
प्रश्न
From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use π = 3.14)
उत्तर
We have,
Height of the cylinder = Height of the cone = h = 15 cm and
Radius of thecylinder = Radius of the cone `= r = 16/2 = 8 "cm" `
Also, the slant height of the cone, `l =sqrt("h"^2 + "r"^2)`
`=sqrt(15^2 + 8^2)`
`=sqrt(225+64)`
`=sqrt(289)`
= 17 cm,
Now,
Then total surface area of the remaining solid = CSA of the cone + CSA of the cone + Area of the base
=πrl+ 2πrh + πr2
= πr (l + 2h + r)
= 3.14 × 8× (17 + 2 × 15 + 8)
= 3.1× 8 × 55
= 1381.6 cm2
So, the total surface area of the remaining solid is 1381.6 cm2.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
APPEARS IN
संबंधित प्रश्न
A solid metallic right circular cone 20 cm high and whose vertical angle is 60°, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/12 cm, find the length of the wire.
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.
Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour ?
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is
Find the surface area of a sphere of radius 3.5 cm.
If the side of a cube is 5 cm, then find its volume.
The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. then height of bucket is ______.
The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?
A tent is a shape of a triangular 'prism' resting on a rectangular side PQ = PR, PT = 1.5 m, QR = 1.8 m, length of the tent = 3 m. Find:
- ∠PQR
- The volume of the tent
