Class 10 Surface Area of Combined Solids — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. When two solids are joined to form a combined solid, the total surface area of the new solid is found by: (CSA = curved surface area, TSA = total surface area)
Aadding the curved/visible surface areas exposed in the combined solid
Badding the total surface areas of both separate solids
Csubtracting the smaller TSA from the larger TSA
Dmultiplying the two surface areas
Show answer
Answer: A) adding the curved/visible surface areas exposed in the combined solid
The faces where the solids join are hidden, so we only add the surfaces that remain exposed (visible) in the combined solid.
2. For a cone, the radius is 6 cm and height is 8 cm. Its slant height is:
A10 cm
B14 cm
C12 cm
D9 cm
Show answer
Answer: A) 10 cm
l = r2+h2 = 36+64 = 100 = 10 cm.
3. Two cubes each of edge 4 cm are joined end to end to form a cuboid. The surface area of the resulting cuboid is:
A160 cm²
B192 cm²
C128 cm²
D176 cm²
Show answer
Answer: A) 160 cm²
Cuboid is 8 x 4 x 4. SA = 2(lb+bh+hl) = 2(8*4 + 4*4 + 4*8) = 2(32+16+32) = 2*80 = 160 cm².
4. A medicine capsule is 14 mm long overall and 5 mm in diameter (so r = 2.5 mm). The cylindrical part length = 14 - 2*2.5 = 9 mm. Its surface area (2*pi*r*h + 4*pi*r²) in mm², taking pi = 722, is approximately:
5. Two cones share a common circular base (a bicone), each of base radius 0.7 cm; the upper cone has slant height 3 cm and the lower cone slant height 5 cm. The total surface area (no base, since it is internal) in cm² (pi = 722) is: