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Surface Areas and Volumes Set-2 MCQ Online Practice Test | Class 10 | Quiz Tweek

Surface Areas and Volumes Set-2

Practice Important MCQs for Surface Areas and Volumes — Maths, Class 10.

This chapter is crucial because it connects geometry with real-world measurements of shapes like cylinders, cones, spheres, and their combinations. Board exams test your ability to apply standard formulas correctly, while competitive exams often test deeper understanding through composite solids, similarity, and “volume remaining/filled” type reasoning. Mastery here strengthens both formula fluency and conceptual problem-solving.

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Q1. A closed cylindrical jar has radius $7\text{ cm}$ and height $10\text{ cm}$ . Find its total surface area. (Use $\text{TSA of a closed cylinder}=2\pi r(h+r)$ .)

(A)

$166\pi\ \text{cm}^2$

(B)

$119\pi\ \text{cm}^2$

(C)

$238\pi\ \text{cm}^2$

(D)

$476\pi\ \text{cm}^2$

Q2. A toy is formed by joining a right circular cone of base radius $5\text{ cm}$ and height $12\text{ cm}$ to a hemisphere of radius $5\text{ cm}$ along their bases. Find the total external surface area of the toy (do not count the common base).

(A)

$115\pi\ \text{cm}^2$

(B)

$130\pi\ \text{cm}^2$

(C)

$95\pi\ \text{cm}^2$

(D)

$150\pi\ \text{cm}^2$

Q3. A hollow spherical shell has outer radius $10\text{ cm}$ and inner radius $8\text{ cm}$ . The material is melted and recast into solid spheres each of radius $2\text{ cm}$ . How many small spheres are obtained?

(A)

$60$

(B)

$62$

(C)

$48$

(D)

$61$

Q4. A right circular cone of base radius $6\text{ cm}$ and height $12\text{ cm}$ is melted and recast into four identical solid spheres. Find the ratio of the total surface area of the four spheres to the curved surface area of the original cone. (Curved surface area of cone = $\pi r l$ , where $l$ is slant height.)

(A)

$2:\sqrt{5}$

(B)

$4:\sqrt{5}$

(C)

$4:5$

(D)

$2\sqrt{5}:5$

Q5. A hole is drilled through the centre of a sphere resulting in a "napkin-ring" (the remaining solid has height $10\text{ cm}$ measured along the axis). Without knowing the original sphere radius, find the volume of the remaining solid. (Hint: volume depends only on the height $h$ of the band.)

(A)

$\dfrac{1000\pi}{3}\ \text{cm}^3$

(B)

$\dfrac{250\pi}{3}\ \text{cm}^3$

(C)

$\dfrac{500\pi}{3}\ \text{cm}^3$

(D)

$\dfrac{125\pi}{3}\ \text{cm}^3$

Q6. A solid is formed by placing a hemisphere on top of a right circular cylinder so that the base of the hemisphere exactly fits the top circular face of the cylinder. The radius of both parts is $5\text{ cm}$ and the height of the cylinder is $14\text{ cm}$ . Find the total surface area of the solid (including the bottom base of the cylinder but excluding the circular interface).

(A)

$190\pi\ \text{cm}^2$

(B)

$215\pi\ \text{cm}^2$

(C)

$225\pi\ \text{cm}^2$

(D)

$240\pi\ \text{cm}^2$

Q7. A conical cup has height $15\text{ cm}$ and rim radius $6\text{ cm}$ . It is filled with water up to a depth of $10\text{ cm}$ . The water wets the inside curved surface of the cone up to that depth. What is the curved surface area of the wetted portion? (Use expressions in simplest radical form.)

(A)

$6\pi\sqrt{125}\ \text{cm}^2$

(B)

$8\pi\sqrt{29}\ \text{cm}^2$

(C)

$10\pi\sqrt{21}\ \text{cm}^2$

(D)

$12\pi\sqrt{13}\ \text{cm}^2$

Q8. A solid sphere of radius $6\text{ cm}$ is melted and recast into identical right circular cones each having base radius $3\text{ cm}$ and height $8\text{ cm}$ . How many such cones can be obtained?

(A)

$9$

(B)

$10$

(C)

$12$

(D)

$15$

Q9. A conical vessel with height $12\text{ cm}$ and base radius $3\text{ cm}$ contains water up to a height of $8\text{ cm}$ . A solid spherical ball is dropped into the vessel and the water just starts to overflow. Find the radius of the spherical ball.

(A)

$\sqrt[3]{24}\ \text{cm}$

(B)

$\sqrt[3]{16}\ \text{cm}$

(C)

$2.5\ \text{cm}$

(D)

$\sqrt[3]{19}\ \text{cm}$

Q10. A right circular cone has slant height $l$ and base radius $r$ . It is cut by a plane parallel to the base producing a smaller similar cone at the top whose slant length is $x$ . Find the value of $x$ in terms of $l$ for which the curved surface area of the smaller top cone equals the curved surface area of the remaining frustum.

(A)

$\dfrac{l}{3}$

(B)

$\dfrac{l}{\sqrt{2}}$

(C)

$\dfrac{l}{2}$

(D)

$\dfrac{2l}{\sqrt{3}}$

Q11. A cylindrical water tank has radius $7\text{ cm}$ . If it contains $2156\pi\ \text{cm}^3$ of water, what is the height of the water level? Use $V=\pi r^2 h$ .

(A)

$22\ \text{cm}$

(B)

$44\ \text{cm}$

(C)

$28\ \text{cm}$

(D)

$77\ \text{cm}$

Q12. A right circular cone of height $24\ \text{cm}$ and base radius $10\ \text{cm}$ is cut by a plane parallel to its base so that the small cone removed at the apex has volume equal to $\tfrac{1}{27}$ of the original cone's volume. What is the height of the remaining frustum? (Use similarity and volume scale factor.)

(A)

$18\ \text{cm}$

(B)

$12\ \text{cm}$

(C)

$16\ \text{cm}$

(D)

$20\ \text{cm}$

Q13. A solid iron sphere of radius $6\ \text{cm}$ is melted and recast into $8$ identical right circular cones each of base radius $3\ \text{cm}$ . Find the height of each cone. (Use $V_{\text{sphere}}=\tfrac{4}{3}\pi r^3$ and $V_{\text{cone}}=\tfrac{1}{3}\pi r^2 h$ .)

(A)

$12\ \text{cm}$

(B)

$9\ \text{cm}$

(C)

$6\ \text{cm}$

(D)

$8\ \text{cm}$

Q14. A solid is formed by attaching a hemisphere of radius $7\ \text{cm}$ to the base of a right circular cone of the same base radius. If the cone's height equals its base radius, the total external surface area of the combined solid (excluding the common circular base) is:

(A)

$49\pi(3+\sqrt{2})\ \text{cm}^2$

(B)

$98\pi(2+\sqrt{2})\ \text{cm}^2$

(C)

$49\pi(2+\sqrt{3})\ \text{cm}^2$

(D)

$49\pi(2+\sqrt{2})\ \text{cm}^2$

Q15. A closed cylindrical container (closed at the bottom) of radius $8\ \text{cm}$ has a hemispherical cap of the same radius fitted on its top so that the hemisphere covers and seals the top. If the total external surface area of this composite solid equals twice the curved surface area of the cylindrical part alone, what is the height of the cylindrical portion? (Take curved surface area of cylinder $=2\pi r h$ , curved area of hemisphere $=2\pi r^2$ , and base area $=\pi r^2$ .)

(A)

$8\ \text{cm}$

(B)

$12\ \text{cm}$

(C)

$16\ \text{cm}$

(D)

$10\ \text{cm}$

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