Advertisements
Advertisements
प्रश्न
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its total surface area.
Advertisements
उत्तर
Here, r1 = 14 cm, r2 = 6 cm and h = 6 cm.
Slant height of the frustum,
l = \[\sqrt{h^2 + \left( r_2 - r_1 \right)^2}\]
= \[\sqrt{6^2 + \left( 14 - 6 \right)^2}\]
= \[\sqrt{6^2 + 8^2}\]
= \[\sqrt{36 + 64}\]
= \[\sqrt{100}\]
= 10 cm
Total surface area of frustrum
\[=\pi l(r_{1}+r_{2})+\pi r_{1}{}^{2}+\pi r_{2}{}^{2}\]
\[ = 3 . 14 \times \left( 14 + 6 \right) \times 10 + 3 . 14 \times {14}^2 + 3 . 14 \times 6^2 \]
\[ = 3 . 14 \times 20 \times 10 + 3 . 14 \times 196 + 3 . 14 \times 36\]
\[ = 628 + 615 . 44 + 113 . 04\]
\[ = 1356 . 48 { cm}^2\]
∴ The total surface area of the frustum is 1356.48 cm2.
APPEARS IN
संबंधित प्रश्न
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. [use π=22/7]
The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is `1/27` of the given cone, then at what height it is cut from its base?
A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone
The radii of the base of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is
A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is
A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.
A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are
20 cm and 12 cm, respectively. Find the height of the bucket. [Use π = 3.14]
A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called
A cylindrical pencil sharpened at one edge is combination of ______.
A cone is cut through a plane parallel to its base and then the cone that is formedon one side of that plane is removed. The new part that is left over on the other side of the plane is called ______.
A solid formed on revolving a right-angled triangle about its height is ______.
The curved surface area of a frustum of a cone is πl (r1 + r2), where `l = sqrt(h^2 + (r_1 + r_2)^2)`, r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.
A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.
