1. The curved surface area of a right circular cylinder is 4400cm sq if the circumference of the base is 110cm, find the height of the cylinder.
2. Find the height of the cone if its slant height is 34cm and base diameter is 32cm.
3. The diameters of two cones are equal if their slant heights are in the ratio 7: 4, find the ratio of their CSA.
4. The outer CSA of hemisphere and sphere are in the ratio 2: 9, find the ratio of their radii.
5. Radius of spherical balloon increases from 6cm to 12cm
Answers
Answer:
These are your answers
Step-by-step explanation:
1) CSA of the cylinder= 4400 square cm
circumference = 110 cm
To find:-
height of the cylinder
solution:-
circumference = 110
=> 2πr =110
=> r = 110*7/2*22
=> r = 35/2
therefore, radius is 35/2 or 17.5
now,
CSA of the cylinder = 4400
=> 2πrh = 4400
=> 2 * 22/7 * 35/2 * h = 4400
=> h = 4400 * 7 * 2 / 2 * 22 *35
=> h = 40 cm
Therefore, the height of the cylinder is 40 cm
2) Slant height l = 34 cm
Diameter d = 32 cm
Radius r = 32/2 = 16 cm
l^2 = (h^2) + (r^2)
(34^2) = (h^2) + (16^2)
1156 = h^2 + 256
h^2 = 1156 - 256
h^2 = 900
h = 30 cm
Hence height = 30 cm
3) Curved surface area = π × r × l
Since the two cones have the same diameter, the radius should be the same (r).
As for the slanted height, since the ratio 7:4 is given, we can assume the slanted height is 7x and 4x. So, we can find the ratio of their curved surface area by eliminate the same factor (π r x) for the two terms (as shown below)
Ratio
= π r (7x) : π r (4x)
= 7:4
Therefore, the ratio between the curved surface area is also equal to 7:4.
4) CSA of hemisphere = 2πr² [r= radius of hemisphere]
CSA of sphere = 4πR² [R=radius of sphere]
thus ratio of their CSA= 2:9
∴2/9 = 2πr²/4πR²
2/9= r²/2R²
2/9×2R²=r²
2×2R²=9×r²
4R²=9r²
r²/R²=4/9
r/R=√4/√9
∴r/R=2/3
ratio of the radii of the hemisphere and sphere
r:R=2:3
5) Surface area of a spherical balloon whose radius is 6 cm.
= 4π × 6 × 6 cm2
Surface area of a spherical balloon whose radius is 12 cm.
= 4π × 12 × 12 cm2
∴ Ration of surface areas = 4π × 6 × 6 / 4π × 12 × 12 = 1 / 4 = 1 : 4