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Surface Area Quiz - CBSE Class 10 Mathematics

Free practice quiz: Surface Area (CBSE Class 10 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 10 Mathematics practice quiz has 11 multiple-choice questions on Surface Area, and 11 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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About this topic

Surface area is the area covering a solid, measured in square units. CSA counts only the curved or side surface; TSA adds the flat bases too. Learn the formula for each solid, then pick CSA or TSA as the question asks.

Surface area is measured in square units like cm², m².
CSA/LSA = curved or side surface only. TSA = CSA + area of base(s).
Cube and cuboid have no curved surface, so LSA means the four side faces.
Cone: slant height l = √(r² + h²). Use l, not h, in CSA and TSA.
Frustum: l = √(h² + (r₁ − r₂)²). TSA adds both circular ends.
Sphere has only curved surface, so CSA = TSA. Hemisphere: CSA 2π r², TSA 3π r² (solid).
Keep all dimensions in the same unit before substituting.

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Cube and Cuboid Surface Areas

Total surface area is the sum of the areas of all six rectangular faces of the solid.
A cube has six equal square faces. Opposite faces of a cuboid are equal in pairs.
If a sphere fits exactly inside a cube, the cube's side equals the sphere's diameter.

TSA of cuboid

\[2(lb + bh + hl)\]

Lateral SA of cuboid

\[2h(l + b)\]

TSA of cube

\[6a^2\]

Lateral SA of cube

\[4a^2\]

Common mistake: Writing a^3 or lbh for surface area. Those formulas give volume, not area.

Cylinder: Curved and Total Area

The curved surface unrolls into a rectangle whose length is the base circumference and whose width is the height.
Total surface area adds the areas of the two circular ends to the curved area.

CSA (lateral) of cylinder

\[2\pi r h\]

TSA of cylinder

\[2\pi r(r + h)\]

Common mistake: Adding the circular ends when only the lateral area is asked. Lateral area means curved surface only.

Cone and Pyramid Using Slant Height

Curved and lateral areas use slant height l, not vertical height h.
For a square pyramid, each of the four triangular faces has base a and height equal to the slant height.

Slant height of cone

\[l = \sqrt{r^2 + h^2}\]

CSA of cone

\[\pi r l\]

TSA of cone

\[\pi r(l + r)\]

TSA of square pyramid

\[a^2 + 2al\]

Common mistake: Using vertical height in place of slant height. Find l from h using Pythagoras first, if needed.

Sphere and Hemisphere

A sphere has only one curved surface. Its area depends only on the radius.
To find the radius from a given area, set the formula equal to the area and solve for r.

SA of sphere

\[4\pi r^2\]

CSA of hemisphere

\[2\pi r^2\]

TSA of hemisphere

\[3\pi r^2\]

Radius from area S

\[r = \sqrt{\frac{S}{4\pi}}\]

Common mistake: Forgetting to take the square root at the end. Solving the equation gives r^2 first, not r.

Frustum of a Cone

A frustum is the part of a cone left after cutting off its top parallel to the base.
Find the slant height using the vertical height and the difference of the two radii.

Slant height

\[l = \sqrt{h^2 + (r_1 - r_2)^2}\]

CSA of frustum

\[\pi (r_1 + r_2) l\]

TSA of frustum

\[\pi (r_1 + r_2) l + \pi r_1^2 + \pi r_2^2\]

Common mistake: Using the sum of the radii inside the slant height formula. Use their difference.

Exam tips

For unknown dimensions, write the surface area formula, substitute the known values, then solve the equation.
Choose \pi = 22/7 when the radius is a multiple of seven. Write the answer in square units.
Read carefully whether the question asks for curved, lateral or total surface area.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the total surface area of a cube with side length 5 cm?
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Answer: D. 150 cm^2
A cube has 6 faces, each of which is a square. The area of one face is side × side = 5 cm × 5 cm = 25 cm^2. Thus, the total surface area is 6 × 25 cm^2 = 150 cm^2.
A cube and a cuboid have the same surface area. The side of the cube is 3 cm. If the dimensions of the cuboid are 2 cm, 3 cm, x cm, what is x?
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Answer: B. 4 cm
The surface area of the cube is 6 × 3² = 54 cm². The surface area of the cuboid is 2(2 × 3 + 3 × x + x × 2). Setting them equal gives 54 = 2(6 + 3x + 2x), solve to find x = 4 cm.
A cylinder has a radius of 7 cm and a height of 20 cm. What is its lateral surface area?
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Answer: C. 880 cm²
The lateral surface area of a cylinder is given by the formula 2πrh. Substituting r = 7 cm, h = 20 cm into the formula gives: 2 × π × 7 × 20 = 880 cm².
What is the curved surface area (CSA) of a cone with a radius of 3 cm and slant height of 7 cm?
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Answer: C. 21π cm²
The curved surface area of a cone is πrl. Substituting the given values: π × 3 × 7 = 21π cm².
Calculate the surface area of a cube circumscribing a sphere of radius 3 cm.
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Answer: B. 324 cm²
The diameter of the sphere is equal to the side of the cube, thus side = 2*radius = 6 cm. The surface area of the cube is 6*side² = 6*6² = 324 cm².

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