Advertisements
Advertisements
प्रश्न
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume
उत्तर
Let the volume of the sphere be V
Let the new volume of the sphere be V'.
`V=4/3pir^3`
`V^I=4/3pir_1^3`
⇒` V^I=4/3pi((11r)/10^3)`
⇒ `V^I=4/3pi1331/1000 r^3`
⇒`v^I=4/3pir^3 1331/1000 `
⇒`V^I=1331/1000 V`
⇒ `V^I=v+1331/1000v`
`⇒ V^I-v=331/1000 v`
∴ Change in volume=`331/10000 v `
`"Percentage change in volume"="Change in volume"/"original volume" xx100`
=`(331/1000V)/Vxx100`
=`331/10`
= 33.1
Percentage change in volume=33.1%
APPEARS IN
संबंधित प्रश्न
A Joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.
A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m2, what will be the cost of painting all these cones. (Use 𝜋 = 3.14 and √1.04 = 1.02)
A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.
The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14).
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitchings. Also, find the cost of the canvas at the rate of Rs. 24 per metre.
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor,
- height of the tent,
- length of the canvas required to cover this conical tent if its width is 2 m.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
A solid metallic cone, with radius 6 cm and height 10 cm, is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as shown and it is completely filled with a lighter metal B. The conical hole has a diameter of 6 cm and depth 4 cm. Calculate the ratio of the volume of metal A to the volume of the metal B in the solid.
The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.
The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 metres deep in the tank. Calculate the volume of water in the tank in gallons.
Curved surface area of a cone is 251.2 cm2 and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)
The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes.
Find the height of the cone whose base radius is 5 cm and volume is 75π cm3.
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: external curved surface area .
A right-angled triangle PQR where ∠Q = 90° is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle
The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.
How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?
