Solid Figures MCQ Quiz - Objective Question with Answer for Solid Figures - Download Free PDF

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

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.

Given:

Edge of solid iron cube = 24 cm

Thickness of rectangular sheet = 2 mm = 0.2 cm

Ratio of length (l) to breadth (b) = 6:5

Formula Used:

Volume of cube = Volume of rectangular sheet

Volume of cube = Edge³

Volume of rectangular sheet = Length × Breadth × Thickness

l / b = 6 / 5

Calculation:

Volume of cube = Edge³

⇒ Volume = 24³

⇒ Volume = 13824 cm³

Volume of rectangular sheet = l × b × 0.2

⇒ 13824 = l × b × 0.2

⇒ l × b = 13824 / 0.2

⇒ l × b = 69120

l / b = 6 / 5

⇒ l = 6k, b = 5k

⇒ l × b = 6k × 5k

⇒ 69120 = 30k²

⇒ k² = 69120 / 30

⇒ k² = 2304

⇒ k = √2304

⇒ k = 48

l = 6k = 6 × 48 = 288 cm

b = 5k = 5 × 48 = 240 cm

l + b = 288 + 240

⇒ l + b = 528 cm

The correct answer is option 2 (528 cm).

Given:

Radius of cylinder = 3 inches.

Height of cylinder = 8 inches.

Formula Used:

Volume of cylinder = πr²h

Volume of hemisphere = (2/3)πr³

Calculation:

Volume of cylinder = π × 3² × 8

⇒ Volume of cylinder = π × 9 × 8

⇒ Volume of cylinder = 72π cubic inches

Volume of hemisphere = (2/3)π × 3³

⇒ Volume of hemisphere = (2/3)π × 27

⇒ Volume of hemisphere = 18π cubic inches

Number of hemispheres = Volume of cylinder / Volume of hemisphere

⇒ Number of hemispheres = 72π / 18π

⇒ Number of hemispheres = 4

The number of hemispheres formed is 4.

Given:

Edge of the wooden cube = 14 cm.

Formula Used:

Volume of the cube = Edge³

Volume of the cone = (1/3) × π × r² × h

Maximum volume of the cone when it is carved from a cube: r = h/2, where h = edge of the cube.

Volume of the removed portion = Volume of the cube - Volume of the cone.

Calculation:

Volume of the cube = Edge³

⇒ Volume of the cube = 14³

⇒ Volume of the cube = 2744 cm³

Radius (r) of the cone = h / 2 = 14 / 2 = 7 cm

Height (h) of the cone = 14 cm

Volume of the cone = (1/3) × π × r² × h

⇒ Volume of the cone = (1/3) × 22/7 × 7² × 14

⇒ Volume of the cone = (1/3) × 22 × 49 × 2

⇒ Volume of the cone = (1/3) × 2156

⇒ Volume of the cone = 718.67 cm³

Volume of the removed portion (V) = Volume of the cube - Volume of the cone

⇒ V = 2744 - 718.67

⇒ V = 2025.33 cm³

3V = 3 × 2025.33

⇒ 3V = 6076 cm³

The value of 3V is 6076 cm³.

Given:

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,

⇒ 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

Given:

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

Given:

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 .

Given:

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

GIVEN:

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.

Given:

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.

GIVEN:

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.                                     

Given:

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

Formula 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.