Surface area of a combination of solids

When two solids are joined, the faces that touch are hidden inside. They are no longer part of the outside. So you add the areas of the faces that stay open, and leave out the joined ones. For round parts, this means using the curved surface area rather than the total.

A small example

Two cubes of side 5 cm are joined end to end. The new solid is a cuboid 10 cm × 5 cm × 5 cm. Its surface area is 2(10 × 5 + 5 × 5 + 10 × 5) = 2 × 125 = 250 cm². Adding the two cubes gives 2 × 150 = 300 cm². The 50 cm² difference is the two hidden faces.

Where marks go

Question 34(A) of CBSE's 2026-27 Maths Standard sample paper is a tent: a cone on top of a cylinder. It asks for the canvas needed. In the 2026-27 Maths Standard marking scheme, the marks go to the parts:

• Half a mark for the cone's height, and 1 mark for its slant height.
• 1 mark for the curved area of the cone, and 1 mark for the curved area of the cylinder.
• Half a mark for the total canvas, and 1 mark for the cost.

The scheme adds the two curved areas and the 26 m² the question allows for stitching and wastage. No flat circles are counted. Each part earns its marks under step marking.

About the author

Mohit Sardana

Chief Architect

An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.

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