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Combination of Solids PYQs

Class 10 Previous Year Questions (2014 – 2026)

Topic Overview

Master the geometry of composite shapes. Remember: Surface Area is the visible area (don't include internal shared bases), while Volume is simply the sum of individual volumes.

Q1 2024
00:00
If two solid hemispheres of same base radius $r$ are joined together along their bases, then curved surface area of the new solid is:
(a)(A) $4\pi r^2$
(b)(B) $3\pi r^2$
(c)(C) $2\pi r^2$
(d)(D) $6\pi r^2$
Joining two hemispheres along their bases forms a complete sphere.
CSA of sphere $= 4\pi r^2$.
Ans: (A) $4\pi r^2$
Q2 2023
00:00
The total surface area of a solid hemisphere of radius $r$ is:
(a)(A) $2\pi r^2$
(b)(B) $3\pi r^2$
(c)(C) $4\pi r^2$
(d)(D) $\pi r^2$
TSA of hemisphere $= CSA + \text{Base Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2$.
Ans: (B) $3\pi r^2$
Q3 2026
00:00
A solid consists of a cylinder of radius 7 cm and height 10 cm, with two cones of same radius and height 5 cm attached at both ends. Find the volume of the solid.
Volume $= \text{Vol(Cyl)} + 2 \times \text{Vol(Cone)}$.
Volume $= \pi(7^2)(10) + 2(1/3)\pi(7^2)(5) = 490\pi + 490\pi/3 = 1960\pi/3 \approx 2053.33$ cm³.
Ans: 2053.33 cm³
Q4 2025
00:00
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
$r = 7$ cm. Height of cylinder $h = 13 - 7 = 6$ cm.
Inner Surface Area $= CSA(\text{hemisphere}) + CSA(\text{cylinder}) = 2\pi r(r+h) = 572$ cm².
Ans: 572 cm²
Q5 2024
00:00
A decorative block is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.
TSA $= 6a^2 - \pi r^2 + 2\pi r^2 = 6a^2 + \pi r^2$.
TSA $= 6(5^2) + (22/7)(2.1)^2 = 150 + 13.86 = 163.86$ cm².
Ans: 163.86 cm²
Q6 2024
00:00
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
Volume $= (2/3)\pi(1)^3 + (1/3)\pi(1)^2(1) = \pi$ cm³.
Ans: $\pi$ cm³
Q7 2022
00:00
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
$r = 3.5, h = 12, l = 12.5$.
TSA $= \pi rl + 2\pi r^2 = 214.5$ cm².
Ans: 214.5 cm²
Q8 2024
00:00
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.
TSA $= 2\pi r(h+2r) = 2(22/7)(3.5)(17) = 374$ cm².
Ans: 374 cm²
Q9 2023
00:00
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Volume of 1 jamun $\approx 25.07$ cm³.
Syrup volume for 45 jamuns $\approx 338$ cm³.
Ans: 338 cm³
Q10 2023
00:00
Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
TSA $= 2\pi r(h+r) = 33000$ cm² $= 3.3$ m².
Ans: 3.3 m²
Q11 2022
00:00
A wooden pen stand is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Vol $= 525 - 4 \times (1/3)\pi(0.5^2)(1.4) = 523.53$ cm³.
Ans: 523.53 cm³
Q12 2026
00:00
From a solid right circular cone, whose height is 6 cm and radius of base is 12 cm, a right circular cylindrical cavity of height 3 cm and radius 4 cm is hollowed out such that the bases of the cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of $\pi$.
Slant height $l = \sqrt{6^2+12^2} = 6\sqrt{5}$.
Area $= CSA(\text{cone}) + \text{Base Area} + CSA(\text{cyl}) + \text{Top Base of cavity}$.
Area $= 72\sqrt{5}\pi + 144\pi + 24\pi + 16\pi = (72\sqrt{5} + 184)\pi$.
Ans: $(72\sqrt{5} + 184)\pi$ cm²
Q13 2026
00:00
PASSAGE: Ice Cream Seller. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top.
(i) Calculate the volume of the cylindrical container.
(ii) Calculate the volume of one such ice-cream cone (including hemispherical top).
(iii) Find the number of such cones which can be filled with ice cream.
(i) $V = \pi(6^2)(15) = 540\pi$ cm³.
(ii) $v = (1/3)\pi(3^2)(12) + (2/3)\pi(3^3) = 36\pi + 18\pi = 54\pi$ cm³.
(iii) Number $= 540\pi / 54\pi = 10$.
Q14 2025
00:00
PASSAGE: Medicine Capsule. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.
(i) Find the radius of the hemispherical part.
(ii) Find the surface area of the entire capsule.
(iii) Find the volume of the capsule.
(i) 2.5 mm. (ii) 220 mm². (iii) 242.16 mm³.
00:00
If two solid hemispheres of same base radius $r$ are joined together along their bases, then curved surface area of the new solid is:
(a)(A) $4\pi r^2$
(b)(B) $3\pi r^2$
(c)(C) $2\pi r^2$
(d)(D) $6\pi r^2$
Joining two hemispheres along their bases forms a complete sphere.
CSA of sphere $= 4\pi r^2$.
Ans: (A) $4\pi r^2$
Q2 2023
00:00
The total surface area of a solid hemisphere of radius $r$ is:
(a)(A) $2\pi r^2$
(b)(B) $3\pi r^2$
(c)(C) $4\pi r^2$
(d)(D) $\pi r^2$
TSA of hemisphere $= CSA + \text{Base Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2$.
Ans: (B) $3\pi r^2$
Q3 2026
00:00
A solid consists of a cylinder of radius 7 cm and height 10 cm, with two cones of same radius and height 5 cm attached at both ends. Find the volume of the solid.
Volume $= \text{Vol(Cyl)} + 2 \times \text{Vol(Cone)}$.
Volume $= \pi(7^2)(10) + 2(1/3)\pi(7^2)(5) = 490\pi + 490\pi/3 = 1960\pi/3 \approx 2053.33$ cm³.
Ans: 2053.33 cm³
Q4 2025
00:00
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
$r = 7$ cm. Height of cylinder $h = 13 - 7 = 6$ cm.
Inner Surface Area $= CSA(\text{hemisphere}) + CSA(\text{cylinder}) = 2\pi r(r+h) = 572$ cm².
Ans: 572 cm²
Q5 2024
00:00
A decorative block is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.
TSA $= 6a^2 - \pi r^2 + 2\pi r^2 = 6a^2 + \pi r^2$.
TSA $= 6(5^2) + (22/7)(2.1)^2 = 150 + 13.86 = 163.86$ cm².
Ans: 163.86 cm²
Q6 2024
00:00
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
Volume $= (2/3)\pi(1)^3 + (1/3)\pi(1)^2(1) = \pi$ cm³.
Ans: $\pi$ cm³
Q7 2022
00:00
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
$r = 3.5, h = 12, l = 12.5$.
TSA $= \pi rl + 2\pi r^2 = 214.5$ cm².
Ans: 214.5 cm²
Q8 2024
00:00
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.
TSA $= 2\pi r(h+2r) = 2(22/7)(3.5)(17) = 374$ cm².
Ans: 374 cm²
Q9 2023
00:00
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Volume of 1 jamun $\approx 25.07$ cm³.
Syrup volume for 45 jamuns $\approx 338$ cm³.
Ans: 338 cm³
Q10 2023
00:00
Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
TSA $= 2\pi r(h+r) = 33000$ cm² $= 3.3$ m².
Ans: 3.3 m²
Q11 2022
00:00
A wooden pen stand is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Vol $= 525 - 4 \times (1/3)\pi(0.5^2)(1.4) = 523.53$ cm³.
Ans: 523.53 cm³
Q12 2026
00:00
From a solid right circular cone, whose height is 6 cm and radius of base is 12 cm, a right circular cylindrical cavity of height 3 cm and radius 4 cm is hollowed out such that the bases of the cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of $\pi$.
Slant height $l = \sqrt{6^2+12^2} = 6\sqrt{5}$.
Area $= CSA(\text{cone}) + \text{Base Area} + CSA(\text{cyl}) + \text{Top Base of cavity}$.
Area $= 72\sqrt{5}\pi + 144\pi + 24\pi + 16\pi = (72\sqrt{5} + 184)\pi$.
Ans: $(72\sqrt{5} + 184)\pi$ cm²
Q13 2026
00:00
PASSAGE: Ice Cream Seller. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top.
(i) Calculate the volume of the cylindrical container.
(ii) Calculate the volume of one such ice-cream cone (including hemispherical top).
(iii) Find the number of such cones which can be filled with ice cream.
(i) $V = \pi(6^2)(15) = 540\pi$ cm³.
(ii) $v = (1/3)\pi(3^2)(12) + (2/3)\pi(3^3) = 36\pi + 18\pi = 54\pi$ cm³.
(iii) Number $= 540\pi / 54\pi = 10$.
Q14 2025
00:00
PASSAGE: Medicine Capsule. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.
(i) Find the radius of the hemispherical part.
(ii) Find the surface area of the entire capsule.
(iii) Find the volume of the capsule.
(i) 2.5 mm. (ii) 220 mm². (iii) 242.16 mm³.