Surface Areas and Volumes

Which statement best summarizes the chapter "Surface Areas and Volumes"?

1. The chapter studies only cubes.
2. The chapter introduces formulas for the surface areas and volumes of cubes, cuboids, cylinders, cones, spheres, hemispheres, and combinations of solids, enabling students to solve practical measurement problems in engineering, architecture, manufacturing, and daily life.
3. The chapter studies only circles.
4. The chapter has no practical applications.

Which theorem is commonly used to find the slant height of a cone?

1. Midpoint Theorem
2. Pythagoras Theorem
3. Basic Proportionality Theorem
4. Angle Bisector Theorem

If the radius of a sphere is doubled, its volume becomes:

1. Double
2. Four times
3. Six times
4. Eight times

A cylinder has:

1. One circular base
2. Two circular bases
3. Three circular bases
4. No circular base

Which solid has one circular base and one curved surface?

1. Sphere
2. Cone
3. Cylinder
4. Cube

Which quantity is measured in square units?

1. Volume
2. Surface Area
3. Height
4. Radius

Which quantity is measured in cubic units?

1. Length
2. Area
3. Volume
4. Perimeter

The volume of a hemisphere is:

1. (2/3)πr³
2. (4/3)πr³
3. πr²
4. 2πrh

The surface area of a sphere is:

1. πr²
2. 2πr²
3. 4πr²
4. (4/3)πr³

The volume of a sphere of radius r is:

1. 4πr²
2. (4/3)πr³
3. πr²
4. 2πr

The curved surface area of a cone is:

1. πrl
2. πr²
3. 2πrh
4. πd

The volume of a cone is:

1. πr²h
2. (1/3)πr²h
3. 2πrh
4. πrl

The total surface area (TSA) of a cylinder is:

1. 2πrh
2. 2πr(r+h)
3. πr²h
4. πr²

The curved surface area (CSA) of a cylinder is:

1. πr²
2. 2πrh
3. 2πr(r+h)
4. (1/3)πr²h

What is the formula for the volume of a cylinder of radius r and height h?

1. 2πrh
2. πr²h
3. πrh
4. 2πr(r+h)

Glass cylinder diameter 20cm, water at 9cm. Metal cube edge 8cm immersed. Rise in water level is

1. 1.6 cm
2. 2 cm
3. 2.6 cm
4. 3 cm

Cone height 8.4cm, radius 2.1cm melted and recast as sphere. Radius of sphere is

1. 1.1cm
2. 2.1 cm
3. 3.0cm
4. 3.5 cm

Three cubes 3,4,5cm melted into single cube. Surface area of new cube is

1. 200cm²
2. 210cm²
3. 216cm²
4. 220cm²

Two cubes of 10cm edge joined end to end. Surface area of cuboid is

1. 900 cm²
2. 1000 cm²
3. 1100 cm²
4. 1200 cm²

Max volume of cone carved from hemisphere of radius r

1. πr³/3
2. πr³/6
3. πr³/2
4. 2πr³/3

Cubes with edges 6,8,10cm melted into single cube. Diagonal of larger cube is

1. 12√3 cm
2. 6√3 cm
3. 13 cm
4. 17 cm

CSA of one cone=2× CSA of other. Slant height of latter=2× former. Ratio of radii is

1. 4:1
2. 3:1
3. 2:1
4. 5:1

Cone height and radius each increased by 50%. Ratio of original to new volume is

1. 8:27
2. 8:28
3. 7:24
4. 6:19

Volume of cone=1570cm³, base area=314cm². Height is

1. 12 cm
2. 13 cm
3. 14 cm
4. 15 cm

Volumes of solid spheres in ratio 125:64. Sum of radii=45cm. Radii are

1. 25, 20
2. 15, 30
3. 35, 10
4. 40, 5

Sum of radius and height=12cm. TSA=540cm². Circumference is

1. 45 cm
2. 40 cm
3. 35 cm
4. 42 cm

CSA of cylinder is 1/3 of TSA. Radius=2.5cm. Height is

1. 2 cm
2. 1.45 cm
3. 1.35 cm
4. 1.25 cm

Volume of water (5cm rain on 2 hectares)

1. 1400m³
2. 1000m³
3. 1200m³
4. 1100m³

Ratio of surface areas of two cubes is 1:9. Ratio of volumes is

1. 1:27
2. 2:27
3. 1:24
4. 1:25

Total surface area of cube is given. Find side.

1. option A
2. option B
3. option C
4. option D

Cone height 9cm, radius 7cm melted into cuboid with two sides 11cm and 6cm. Third side is

1. 5 cm
2. 6 cm
3. 7 cm
4. 10 cm

LMNO and GHJK rectangles, GH=LM, HJ=MN/2. Fraction of LMNO not shaded is

1. 3/4
2. 1/2
3. 1/4
4. 3/4

Two cones height 2cm each, upper full of water, water drips to lower. When upper has 1cm water, height in lower is

1. 7^(1/3) cm
2. (7)^(1/3)
3. (7/8)^(1/3)×2
4. 1 cm

Vertical and horizontal cross-sections of right circular cylinder are

1. square, circle
2. rectangle, circle
3. rectangle, square
4. rectangle, ellipse

Metal pipe 77cm long, inner diameter 4cm, outer diameter 4.5cm, density 8g/cm³. Weight is

1. 205.7 kg
2. 20.57 kg
3. 2.057 kg
4. 207.20 kg

Circus tent = cone over cylinder, diameter 9m, cylinder height 4.8m, total height 10.8m. Canvas required is

1. 241.84m²
2. 24.184m²
3. 2418.4m²
4. 2478.4m²

Frustum cone radii 28cm and 7cm, height 45cm. Capacity is

1. 48105cm²
2. 48510cm²
3. 48150cm²
4. 48769cm²

Hollow sphere internal diameter 4cm, external diameter 8cm, melted into cone, base diameter 8cm. Height of cone is

1. 14 cm
2. 12 cm
3. 16 cm
4. 18 cm

27 buckets (radius 14cm, height 16cm) of lime poured into conical heap area 5544cm². Canvas to cover is

1. 19800cm²
2. 198cm²
3. 1980cm²
4. 1978cm²

Cylindrical vessel diameter 9cm; cylindrical iron piece diameter 6cm, height 4.5cm dropped in. Rise in water level is

1. 0.1 cm
2. 0.5 cm
3. 0.8 cm
4. 0.7 cm

Top = cone over hemisphere, r=3.5cm, total height=15.5cm. Total area is

1. 215.4cm²
2. 21.45cm²
3. 214.5cm²
4. 285.45cm²

Hemisphere inner diameter 9cm filled with liquid, poured into cylindrical bottles diameter 3cm, height 4cm. Bottles required are

1. 54
2. 45
3. 50
4. 58

From circle radius 15cm, sector angle 216° cut out and bent into cone. Volume is

1. 1071.3cm³
2. 1081cm³
3. 1018.3cm³
4. 1087cm³

Conical vessel, volume 33.264L, height 72cm. Cost of repairing CSA at Rs12/sq.m is

1. Rs 5.94
2. Rs 6.94
3. Rs 7.95
4. Rs 8.98

Cuboid 44×30×15cm melted into cylinder of height 28cm. Radius is

1. 10 cm
2. 20 cm
3. 15 cm
4. 12 cm

Curved surface painted at Rs5/cm² costs Rs3520. Slant height 25cm. Volume of cone is

1. 1232cm³
2. 1332cm³
3. 1223cm³
4. 1323cm³

Base area of cone is 616cm², height 48cm. Total surface area is

1. 2681cm²
2. 2861cm²
3. 2816cm²
4. 2874cm²

Ratio of curved surface areas of two cylinders with equal radii

1. H²:h²
2. 2H:h
3. H:h
4. H²:h

Ratio of volumes of two cones with same height

1. r₁²:r₂²
2. r₁:r₂
3. r₁³:r₂³
4. r₁:3r₂

Cylinder contains 49.896L, painting CSA costs 2p/cm² = Rs95.04. Total surface area is

1. 5742cm²
2. 7524cm²
3. 5724cm²
4. 7584cm²

Cone radius:height=3:4. Smoothening curved surface at 5p/cm² costs Rs11550. Volume is

1. 12936cm³
2. 12693cm³
3. 12963cm³
4. 12878cm³

Ratio of lateral surface areas of two cylinders with equal heights

1. R:r
2. H:h
3. R²:r²
4. H²:h

Lateral surface area of cylinder radius 7cm, height 10cm is

1. 240cm²
2. 404cm²
3. 440cm²
4. 165cm²

Lateral surface area 176cm², base area 38.5cm². Volume is

1. 803cm³
2. 380cm³
3. 308cm³
4. 830cm³

Total surface area of cylinder is 220cm², height 6.5cm. Volume is

1. 25.026cm³
2. 2.5025cm³
3. 2502.5cm³
4. 250.25cm³