R.d Sharma 2022 _mcqs Solutions for Class 9 Maths Chapter 19 Surface Area And Volume Of A Right Circular Cylinder are provided here with simple step-by-step explanations. These solutions for Surface Area And Volume Of A Right Circular Cylinder are extremely popular among Class 9 students for Maths Surface Area And Volume Of A Right Circular Cylinder Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 _mcqs Book of Class 9 Maths Chapter 19 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 _mcqs Solutions. All R.d Sharma 2022 _mcqs Solutions for class Class 9 Maths are prepared by experts and are 100% accurate.
Page No 197:
Question 1:
In a cylinder, if radius is doubled and height is halved, curved surface area will be
(a) halved
(b) doubled
(c) same
(d) four times
Answer:
Let radius be 'r' and height be 'h'
∴ Original Curved Surface Area =
Thus, if the radius is doubled and the height is halved in a cylinder, the curved surface area will be the same.
Hence, the correct answer is option (c).
Page No 197:
Question 2:
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
(a) 1 : 4
(b) 1 : 3
(c) 3 : 1
(d) 2 : 5
Answer:
Let V1 and V2 be the volume of the two cylinders with radius r1 and height h1, and radius r2 and height h2, where
So,
Now,
From equation (1) and (2), we have
Thus, the ratio of their volumes is 3 : 1.
Hence, the correct answer is option (c).
Page No 197:
Question 3:
The number of surfaces in right cylinder is
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
A right cylinder has one curved and two flat surfaces.
Thus, the number of surfaces in a right cylinder is 3.
Hence, the correct answer is option (c).
Page No 197:
Question 4:
Vertical cross-section of a right circular cylinder is always a
(a) square
(b) rectangle
(c) rhombus
(d) trapezium
Answer:
From the following figure of a cylinder, it can be observed that the vertical cross section is the rectangle PQRS.
Thus, vertical cross-section of a right circular cylinder is always a rectangle.
Hence, the correct answer is option (b).
Page No 197:
Question 5:
If r is the radius and h is height of the cylinder the volume will be
(a)
(b) πr2h
(c) 2πr(h + r)
(d) πrh
Answer:
Given: r is the radius and h is the height of the cylinder.
The volume of a cylinder is given by the formula
Hence, the correct answer is option (b).
Page No 197:
Question 6:
The number of surfaces of a hollow cylindrical object is
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
In a hollow cylinder, there are two curved surface areas: inner and outer and one circular base with inner and outer surface area.
Thus, there are 4 surfaces in a hollow cylindrical object.
Hence, the correct answer is option (d).
Page No 197:
Question 7:
If the radius of a cylinder is doubled and the height remains same, the volume will be
(a) doubled
(b) halved
(c) same
(d) four times
Answer:
Let V1 be the volume of the cylinder with radius r1 and height h1, then
Now, let V2 be the volume after changing the dimension, then
So,
Hence, the correct answer is option (d).
Page No 197:
Question 8:
If the height of a cylinder is doubled and radius remains the same, then volume will be
(a) doubled
(b) halved
(c) same
(d) four times
Answer:
Let V1 be the volume of the cylinder with radius r1 and height h1, then
.…. (1)
Now, let V2 be the volume after changing the dimension, then
So,
Hence, the correct answer is option (a).
Page No 197:
Question 9:
In a cylinder, if radius is halved and height is doubled, the volume will be
(a) same
(b) doubled
(c) halved
(d) four times
Answer:
Let V1 be the volume of the cylinder with radius r1 and height h1, then
Now, let V2 be the volume after changing the dimension, then
So,
Hence, the correct answer is option (c).
Page No 197:
Question 10:
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is
(a) 2πh2
(b)
(d)
(d) πh2
Answer:
Let r be the radius of the cylinder and h be its height
∴Total surface area (S)
Hence, the correct answer is option (b).
Page No 197:
Question 11:
A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m2, is
(a) 40π
(b) 80π
(c) 160π
(d) 200π
Answer:
Diameter of right circular cylindrical tunnel (d) = 2 m
Radius of right circular cylindrical tunnel (r) = m
Height of right circular cylindrical tunnel (h) = 40 m
∴ The area of the iron sheet required = Surface area of the cylinder
Hence, the correct answer is option (b).
Page No 197:
Question 12:
Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is
(a)
(b)
(c) 1 : 2
(d) 1 : 4
Answer:
Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights.
Let r1 and r2 be their base radius.
Hence, the correct answer is option (b).
Page No 197:
Question 13:
The radius of a wire is decreased to one-third. If volume remains the same, the length will become
(a) 3 times
(b) 6 times
(c) 9 times
(d) 27 times
Answer:
Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights.
Let r1 and r2 be their base radius.
Thus, the length will become 9 times.
Hence, the correct answer is option (c).
Page No 197:
Question 14:
If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?
(a) 4
(b)
(c) 2
(d)
Answer:
Let V1 be the volume of the cylinder with radius r1 and height h1, then
Now, let V2 be the volume after changing the dimension, then
Thus, the radius of the base should be multiplied by so that the resulting cylinder has the same volume as the original cylinder.
Hence, the correct answer is option (b).
Page No 198:
Question 15:
The volume of a cylinder of radius r is of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?
(a)
(b)
(c)
(d)
Answer:
Let V1 be the volume of the cylinder with radius r and height h, then
.…. (1)
Now, let V2 be the volume of the box, then
∵ V1 = V2
Hence, the correct answer is option (b).
Page No 198:
Question 16:
The height h of a cylinder equals the circumference of the cylinder. In terms of h, what is the volume of the cylinder?
(a)
(b)
(c)
(d) πh3
Answer:
Let h be the height of the cylinder with radius r.
The height h of a cylinder equals the circumference of the cylinder
Hence, the correct answer is option (a).
Page No 198:
Question 17:
A cylinder with radius r and height h is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?
(a) 2πr(r + h)
(b) πr(r + 2h)
(c) πr(2r + h)
(d) 2πr2 + h
Answer:
Let S be the total surface area of the closed cylinder with radius r and height h, then
Hence, the correct answer is option (a).
Page No 198:
Question 18:
The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
(a)
(b)
(c)
(d)
Answer:
Let r be the radius of the cylinder. It is given that the height drops 3 inches when 1 cubic foot of sand is poured out and 1 foot = 12 inch
Thus, the diameter of the cylinder is inches.
Hence, the correct answer is option (b).
Page No 198:
Question 19:
Two steel sheets each of length a1 and breadth a2 are used to prepare the surfaces of two right circular cylinders — one having volume v1 and height a2 and other having volume v2 and height a1. Then,
(a) v1 = v2
(b) a1v1 = a2v2
(c) a2v1 = a1v2
(d)
Answer:
Let the radius of the base of the cylinders be r and R.
Now, let the sheet with length a1 be used to form a cylinder with volume v1.
So,
Volume
Similarly, let sheet with length a2 be used to form a cylinder with volume v2.
Volume
Now,
Hence, the correct answer is option (c).
Page No 198:
Question 20:
The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is
(a)
(b)
(c)
(d) 2
Answer:
Let the radius and height of the original circular cylinder be r and h and the radius and height of the new circular cylinder be R and H.
H = 6h (Given) .....(1)
Base area of the original circular cylinder (a) = .....(2)
Base area of the new circular cylinder (A) = .....(3)
∵ Base area of the new circular cylinder (A) = Base area of the original circular cylinder (a)
Lateral surface area of the original circular cylinder (s) = .....(5)
Lateral surface area of the new circular cylinder (S) =
Thus, the factor by which the lateral surface of the cylinder increases, is 2.
Hence, the correct answer is option (d).
Page No 198:
Question 21:
The volume of a cuboid is 64 cm3. The length, breadth and height have integral values in cm. If the breadth is not less than its height, then the minimum possible lateral surface area of the
cuboid is
(a) 32 cm2
(b) 36 cm2
(c) 40 cm2
(d) 50 cm2
Answer:
Given: The volume of cuboid = 64 cm3 .....(1)
Let l, b and h be the length, breadth and height of the cuboid.
The volume of cuboid = l × b × h .....(2)
From (1) and (2), we get
l × b × h = 64 cm3
The possible 3 numbers whose multiplication will result in 64 are
Case I: 1 × 8 × 8
Case II: 2 × 4 × 8
Case III: 4 × 4 × 4
Case IV: 1 × 4 ×16
Case V: 1 × 2× 32
Lateral surface area of cuboid = 2 × (l + b)× h
All the possible lateral surface area of the cuboid are
Case I: l = 8, b = 8, h = 1
⇒ Lateral surface area of cuboid = 2 × (8 + 8) × 1
= 2 ×16
= 32 cm2
Case II: l = 8, b = 4, h = 2
⇒ Lateral surface area of cuboid = 2 × (8 + 4) × 2
= 2 × 12 × 2
= 48 cm2
Case III: l = 4, b = 4, h = 4
⇒ Lateral surface area of cuboid = 2 × (4 + 4) × 4
= 2 × 8 × 4
= 64 cm2
Case IV: l = 16, b = 4, h = 1
⇒ Lateral surface area of cuboid = 2 × (16 + 4) × 1
= 2 × 22 × 1
= 44 cm2
Case V: l = 32, b = 2, h = 1
⇒ Lateral surface area of cuboid = 2 × (32 + 2) × 1
= 2 × 34 × 1
= 68 cm2
Thus, the minimum possible lateral surface area of the cuboid is 32 cm2.
Hence, the required answer is option (a).
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