Solid Figures MCQ Quiz - Objective Question with Answer for Solid Figures - Download Free PDF
Last updated on Jun 15, 2025
Latest Solid Figures MCQ Objective Questions
Solid Figures Question 1:
A rectangular sheet of 31.4 cm x 10 cm size is rolled across its length to make a cylinder without overlap. What will be the approximate volume of the cylinder?
Answer (Detailed Solution Below)
Solid Figures Question 1 Detailed Solution
Given:
Length of rectangular sheet = 31.4 cm
Breadth of rectangular sheet = 10 cm
Formula used:
Circumference of the base of the cylinder = Length of the sheet
Height of the cylinder = Breadth of the sheet
Volume of the cylinder = π × r2 × h
Where, r = radius of the base, h = height
Calculation:
Length of the sheet = Circumference of the base = 2πr
⇒ 31.4 = 2 × 3.14 × r
⇒ r = 31.4 / (2 × 3.14)
⇒ r = 5 cm
Height of the cylinder = Breadth of the sheet = 10 cm
Volume of the cylinder = π × r2 × h
⇒ Volume = 3.14 × (5)2 × 10
⇒ Volume = 3.14 × 25 × 10
⇒ Volume = 785 cm3
∴ The correct answer is option (1).
Solid Figures Question 2:
The combined perimeter of the top and bottom circular faces of a right circular cylinder is 176 cm. The volume of the cylinder is given as 3528π cm³. If the height of the cylinder is three-fourths the length of a side of a square, what is the area of the square (in cm²)?
Answer (Detailed Solution Below)
Solid Figures Question 2 Detailed Solution
Calculation
ATQ, 2 ×(2πr) = 176
Or, 2πr = 88
Or, πr = 44
So, r = 14 cm
Volume of the cylinder = [22/7] r2h = 3528π
So, 196h = 3528
So, h = 18
Side of the square = 18 × [4 / 3] = 24 cm
Required area = 24 × 24 = 576 cm
Solid Figures Question 3:
If the diameter of a sphere is increased by 30%, then increase in the surface area is
Answer (Detailed Solution Below)
Solid Figures Question 3 Detailed Solution
Given:
The diameter of a sphere is increased by 30%.
Formula used:
Surface area of a sphere = 4πr2
Where r is the radius of the sphere.
Calculations:
Let the original diameter of the sphere be D, and the original radius be r = D/2.
So, the original surface area = 4πr2.
Now, if the diameter is increased by 30%, the new diameter is:
New diameter = D × (1 + 30/100) = 1.30D
The new radius is:
New radius = 1.30 × r = 1.30r.
The new surface area is:
New surface area = 4π(1.30r)2 = 4π × 1.69r2 = 1.69 × (4πr2).
The increase in the surface area is:
Increase = 1.69 × (original surface area) - original surface area
⇒ Increase = (1.69 - 1) × (original surface area)
⇒ Increase = 0.69 × (original surface area).
∴ The increase in the surface area is 69%.
Solid Figures Question 4:
A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs. 25 per metre square. [Use π = 22/7]
Answer (Detailed Solution Below)
Solid Figures Question 4 Detailed Solution
Given:
breadth = 5 m
diameter = 14 m
height = 24 m
Rate = Rs. 25/m
Formula used:
CSA(Cone) = 22/7 x r x l
l2 = h2 + r2
r = radius of the cone/tent(here)
h = slant height
CSA = Curved Surface Area
Solution:
r = 14/2 = 7 m
l = \(\sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625}\)
l = 25 m
CSA = 22/7 x 7 x 25
CSA = 550 m2
Cost of cloth required = 550 x 25 = Rs. 13750
Hence, the correct option is 2.
Solid Figures Question 5:
A large cube with a side length of 28 meters is melted to form n small cubes and 7 medium cubes. From another large cube of same size, 16 small cubes and m medium cubes are formed. In both cases, the dimensions of the small and medium cubes remain consistent. If the side length of a small cube is 7 meters and that of a medium cube is 14 meters, then what is the value of n + m?
Answer (Detailed Solution Below)
Solid Figures Question 5 Detailed Solution
Calculation
Given:
Large cube side = 28 m
Small cube side = 7 m
Medium cube side = 14 m
First large cube gives: n small + 7 medium cubes
Second identical cube gives: 16 small + m medium cubes
We are to find n + m
Volume of large cube = 283 = 28 × 28 × 28 = 21952 m3
Volume of small cube = 73 = 343 m3
Volume of medium cube = 143 = 2744 m3
n × 343 + 7 × 2744 = 21952
n × 343 + 19208 = 21952
⇒ n × 343 = 2744
⇒n = 2744/343 = 8
16 × 343 + m × 2744 = 21952
⇒ 5488 + m × 2744 = 21952
⇒ m × 2744 = 16464
⇒ m = 16464/2744 = 6
So, n + m = 8 + 6 = 14
The correct answer is Option (2).
Top Solid Figures MCQ Objective Questions
A solid hemisphere has radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2 ∶ 5. What is the radius (in cm) of its base (take π = \(\frac{{22}}{7}\))?
Answer (Detailed Solution Below)
Solid Figures Question 6 Detailed Solution
Download Solution PDFGiven:
The radius of a solid hemisphere is 21 cm.
The ratio of the cylinder's curved surface area to its Total surface area is 2/5.
Formula used:
The curved surface area of the cylinder = 2πRh
The total surface area of cylinder = 2πR(R + h)
The volume of the cylinder = πR2h
The volume of the solid hemisphere = 2/3πr³
(where r is the radius of a solid hemisphere and R is the radius of a cylinder)
Calculations:
According to the question,
CSA/TSA = 2/5
⇒ [2πRh]/[2πR(R + h)] = 2/5
⇒ h/(R + h) = 2/5
⇒ 5h = 2R + 2h
⇒ h = (2/3)R .......(1)
The cylinder's volume and the volume of a solid hemisphere are equal.
⇒ πR2h = (2/3)πr3
⇒ R2 × (2/3)R = (2/3) × (21)3
⇒ R3 = (21)3
⇒ R = 21 cm
∴ The radius (in cm) of its base is 21 cm.
The surface area of three faces of a cuboid sharing a vertex are 20 m2, 32 m2 and 40 m2. What is the volume of the cuboid?
Answer (Detailed Solution Below)
Solid Figures Question 7 Detailed Solution
Download Solution PDFThe surface area of three faces of a cuboid sharing a vertex are 20 m2, 32 m2 and 40 m2,
⇒ L × B = 20 sq. Mt
⇒ B × H = 32 sq. Mt
⇒ L × H = 40 sq. Mt
⇒ L × B × B × H × L × H = 20 × 32 × 40
⇒ L2B2H2 = 25600
⇒ LBH = 160
∴ Volume = LBH = 160 m3A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
Answer (Detailed Solution Below)
Solid Figures Question 8 Detailed Solution
Download Solution PDFGiven:
Each side of the cube = 8 cm
The rectangular container has a length of 16 cm, breadth of 8 cm, and height of 15 cm
Formula used:
The volume of cube = (Edge)3
The volume of a cuboid = Length × Breadth × Height
Calculation:
The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise
Let, the height of the water level will rise = x cm
So, 83 = 16 × 8 × x
⇒ 512 = 128 × x
⇒ x = 512/128 = 4
∴ The rise of water level (in cm) is 4 cm
The sum of length, breadth and height of a cuboid is 21 cm and the length of its diagonal is 13 cm. Then the total surface area of the cuboid is
Answer (Detailed Solution Below)
Solid Figures Question 9 Detailed Solution
Download Solution PDFGiven:
Sum of length,, breadth and height of a cuboid = 21 cm
Length of the diagonal(d) = 13 cm
Formula used:
d2 = l2 + b2 + h2
T.S.A of cuboid = 2(lb + hb +lh)
Calculation:
⇒ l2 + b2 + h2 = 132 = 169
According to question,
⇒ (l + b + h)2 = 441
⇒ l2 + b2 + h2 + 2(lb + hb +lh) = 441
⇒ 2(lb + hb +lh) = 441 - 169 = 272
∴ The answer is 272 cm2 .
Three cubes with sides in the ratio of 3 ∶ 4 ∶ 5 are melted to form a single cube whose diagonal is 18√3 cm. The sides of the three cubes are:
Answer (Detailed Solution Below)
Solid Figures Question 10 Detailed Solution
Download Solution PDFGiven:
Three cubes with sides in the ratio of 3 ∶ 4 ∶ 5 are melted to form a single cube whose diagonal is 18√3 cm.
Concept used:
The diagonal of a cube = √3a (where a is the sides)
Calculation:
Let the s sides of the cubes will be 3x cm , 4x cm, and 5x cm
As per the question,
Volume of the new cube is
(3x)3 +( 4x)3 +( 5x)3 = 216 x3.
⇒ side is = 6x
diagonal is 6x√3
⇒ 6x√3 = 18√3
⇒ x = 3
The sides of the cubes will be 9 cm , 12 cm, and 15 cm
∴ The correct option is 2
If the surface area of a sphere is 1386 cm2, then find the radius of the sphere.
Answer (Detailed Solution Below)
Solid Figures Question 11 Detailed Solution
Download Solution PDFGIVEN:
The surface area of a sphere = 1386 \(cm^2\)
FORMULA USED:
The surface area of a sphere = 4πr2where r is the radius of the sphere.
CALCULATION:
The surface area of a sphere =4πr2 = 1386
⇒ 4 × (22/7) × r2 = 1386 ....(value of \(\pi\) is \(\frac{22}{7}\))
⇒ r2 = 110.25
⇒ r2 = \(\frac{11025}{100}\)
⇒ r = \(\sqrt\frac{11025}{100}\) = \(\frac{105}{10}\) = 10.5 cm.
∴ The radius of the sphere is 10.5 cm.
A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is:
Answer (Detailed Solution Below)
Solid Figures Question 12 Detailed Solution
Download Solution PDFGiven:
The curved surface area of the cone = 2 × base area of cone
Concepts used:
Formula used
Slant height (l) of cone = √r2 + h2
CSA of cone = πrl
Calculation:
Let the radius of the cone be r units.
⇒ πrl = 2πr2
⇒ l = 2r
⇒ r = 6√3/2
⇒ r = 3√3
Slant height (l) of cone = √r2 + h2
⇒ 6√32 = 3√32 + h2
⇒ h2 = 108 - 27 = 81
⇒ h = 9 cm
∴ The answer is 9 cm.
To pack a set of books, Gautam got cartons of a certain height that were 48 inches long and 27 inches wide. If the volume of such a carton was 22.5 cubic feet, what was the height of each carton? [Use 1 foot = 12 inches.]
Answer (Detailed Solution Below)
Solid Figures Question 13 Detailed Solution
Download Solution PDFGIVEN:
Cartons having length = 48 inches and breadth = 27 inches
The volume of cartoon = 22.5 cubic feet.
FORMULA USED :
Volume of Cuboid = Length × Breadth × Height
CALCULATION :
Volume of carton = volume of cuboid = Length × Breadth × Height
⇒ volume of carton = 48 × 27 × Height
∵ 1 foot = 12 inches, then 22.5 cubic feet = 22.5 × 12 × 12 ×12
⇒ 22.5 × 12 × 12 × 12 = 48 × 27 × Height
⇒ 38,880 = 1,296 × Height
⇒ Height = 30 inches.
∴ The height of each cartoon is 30 inches.
A sphere of radius 42 cm is melted and recast into a cylindrical wire of radius 21 cm. Find the length of the wire.
Answer (Detailed Solution Below)
Solid Figures Question 14 Detailed Solution
Download Solution PDFGiven:
Radius of Sphere = 42 cm
Radius of wire = 21 cm
Formula:
Volume of cylinder = πr2h
Volume of sphere = [4/3]πr3
Calculation:
Let length of the wire be x, then
According to the question
π × 21 × 21 × x = [4/3] × π × 42 × 42 × 42 [As volume will remain constant]
⇒ x = (4 × 42 × 42 × 42)/(21 × 21 × 3)
⇒ x = 224 cm
∴ The length of the wire is 224 cm
A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:
Answer (Detailed Solution Below)
Solid Figures Question 15 Detailed Solution
Download Solution PDFFormula Used:
Volume of sphere = \(\frac{4}{3}\)πr3
Surface area of sphere = 4πr2
Calculation:
If the radius of a smaller sphere be 'r cm' then
Acoording to the question:
\(\frac{4}{3}\)π(10)3 = 1000\(\frac{4}{3}\)π(r)3
r = 1 cm
Surface area of the larger sphere = 4π(10)2 = 400π
Total surface area of 1000 smaller spheres = 1000 × 4π(1)2 = 4000π
Net increase in the surface area = 4000π − 400π = 3600π
Hence, surface area of the metal is increased by 9 times.