CBSE Class 10 Mathematics Surface Area and Volume Assignment Set D

Question. The volume of cylindrical cup is
(a) 295.75 cm³
(b) 7415.5 cm³
(c) 384.88 cm³
(d) 404.25 cm³

Answer: D

Question. The volume of hemispherical cup is
(a) 179.67 cm³
(b) 89.83 cm³
(c) 172.25 cm³
(d) 210.60 cm³

Answer: B

Question. Which container had more juice and by how much?
(a) Hemispherical cup, 195 cm³
(b) Cylindrical glass, 207 cm³
(c) Hemispherical cup, 280.85 cm³
(d) Cylindrical glass, 314.42 cm³

Answer: D

Question. The height of the conical tent prepared to accommodate four students is
(a) 18m
(b) 10m
(c) 24m
(d) 14m

Answer: C

Question. How much space on the ground is occupied by each student in the conical tent
(a) 54 m²
(b) 38.5 m²
(c) 86 m²
(d) 24 m²

Answer: B

Case /Passage-II

The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BCE. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha. .It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal structure mounted on it. (Take π = 22/7)

Question. Calculate the volume of the hemispherical dome if the height of the dome is 21 m –
(a) 19404 cu. m
(b) 2000 cu .m
(c) 15000 cu. m
(d) 19000 cu. m

Answer: A

Question. The formula to find the Volume of Sphere is-
(a) (2/3) πr³
(b) (4/3) πr³
(c) 4 πr³
(d) 2 πr³

Answer: B

Question. The cloth require to cover the hemispherical dome if the radius of its base is 14m is
(a) 1222 sq.m
(b) 1232 sq.m
(c) 1200 sq.m
(d) 1400 sq.m

Answer: C

Question. The total surface area of the combined figure i.e. hemispherical dome with radius 14m and cuboidal shaped top with dimensions 8m × 6m × 4m is
(a) 1200 sq. m
(b) 1232 sq. m
(c) 1392 sq.m
(d) 1932 sq. m

Answer: C

Question. The volume of the cuboidal shaped top is with dimensions mentioned in question 4
(a) 182.45 m³
(b) 282.45 m³
(c) 292 m³
(d) 192 m³

Answer: D

Case /Passage-III

On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and you wanted them to buy a RUBIK’s cube and strawberry ice-cream for you. Observe the figures and answer the questions-:

Question. The length of the diagonal if each edge measures 6cm is
(a) 3√3
(b) 3√6
(c) √12
(d) 6√3

Answer: D

Question. Volume of the solid figure if the length of the edge is 7cm is-
( a) 256 cm³
(b) 196 cm³
(c) 343 cm³
(d) 434 cm³

Answer: C

Question. What is the curved surface area of hemisphere (ice cream) if the base radius is 7cm?
(a) 309 cm²
(b) 308 cm²
(c) 803 cm²
(d) 903 cm²

Answer: B

Question. Slant height of a cone if the radius is 7cm and the height is 24 cm
(a) 26cm
(b) 25 cm
(c) 52 cm
(d) 62 cm

Answer: B

Question. The total surface area of cone with hemispherical ice cream is
(a) 858 cm²
(b) 885 cm²
(c) 588 cm²
(d) 855 cm²

Answer: A

Assertion & Reason

DIRECTIONS : Each of these questions contains an Assertion followed by Reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements.
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion: Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm².
Reason: If r be the radius and h be the height of the cylinder, then total surface area = (2πrh + 2πr² ).
Answer: A

Question.  Assertion: If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Reason: If r be the radius and h the slant height of the cone, then slant height = √h²+r² .
Answer: D

Question. Assertion: If the radius of a cone is halved and volume is not changed, then height remains same.
Reason: If the radius of a cone is halved and volume is not changed then height must become four times of the original height.
Answer: D

Question. Assertion: If a ball is in the shape of a sphere has a surface area of 221.76 cm², then its diameter is 8.4 cm.
Reason: If the radius of the sphere be r, then surface area, S = 4πr², i. e. r = 1/2 √S/π.
Answer: A

Question. Assertion: No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541
Reason : Number of balls = Volume of one ball / volumeof lead
Answer: C

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. The volume of a cube with diagonal d is .............
Answer: d³/3√3 cb. units.

Question. A cube is a special type of ..............
Answer: cuboid

Question. If the heights of two cylinders are equal and their radii are in the ratio of 7 : 5, then the ratio of their volumes is .................
Answer: 49 : 25

Question. The volume of a solid is the measurement of the portion of the ............ occupied by it.
Answer: space

Question. If the volume of a cube is 64 cm3, then its surface area is ....................
Answer: 96 cm²

Question. If the volume and the surface area of a solid sphere are numerically equal, then its radius is .........
Answer: 3 units

Question. The length of the diagonal of a cube that can be inscribed in a sphere of radius 7.5 cm is ............ True / False
Answer: 15 cm

DIRECTIONS : Read the following statements and write your answer as true or false.

Question. Volume of the solid is measured in cubic units.
Answer: True

Question. Area is the length of the boundary of a closed figure.
Answer: False

Question. Area is the total surface covered by a closed figure.
Answer: True

Question. The volume of sphere of diameter is πd³/6.
Answer: True

Question. The total surface area of a solid cylinder of radius r and height h is 2π r (h + r).
Answer: True

Question. If a right circular cone and a cylinder have equal circles as their base and have equal heights, then the ratio of their volumes is 2 : 3
Answer: False

Question. If the base area and the volume of a cone are numerically equal, then its height is 3 units.
Answer: True

Question. If the curved surface of a right circular cylinder is 1760 cm2 and its radius is 21 cm, then its height is (80/3) cm.
Answer: False

Question. If the total surface area of a cube is (50/3)m2 , then its side is (5/3) m.
Answer: True