TEST-IX (VOLUME & SURFACE AREAS)
Q1. A joker¢s cap is in the form of a right
circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet
required to make 10 such caps?
Q2. A sphere is
tightly enclosed in a cylinder. Find ratio of curved surface area of cylinder
to sphere?
Q3. A right
triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm.
Find the volume of the solid so
obtained?
SECTION-B (3
MARKS QUESTIONS)
Q4. Monica has a
piece of canvas whose area is 551 m2. She uses it to have a conical
tent made, with a base radius of 7 m. Assuming that all the stitching margins
and the wastage incurred while cutting, amounts to approx. 1 m2,
find the volume of the tent that can be made with it.
Q5. Twenty seven
solid iron spheres, each of radius r and surface area S are melted to form a sphere
with surface area S¢. Find the: (i) radius r¢ of the new
sphere, (ii) ratio of S and S¢.
Q6. The diameter
of a roller is 84 cm and its length is 120 cm. It takes 500 complete
revolutions to move once over to level a playground. Find the area of the
playground in m2 ?
Q7. Three solid
spheres of iron whose diameters are 2 cm, 12 cm and 16 cm, respectively, are
melted into a single solid sphere. Find the radius of the solid sphere.
SECTION-C (4
MARKS QUESTIONS)
Q8. A small
indoor greenhouse is made entirely of glass panes held together with tape. It
is 30 cm long, 25 cm wide and 25 cm high.
(i) What is the area of the glass?
(ii) How
much of tape is needed for all the 12 edges?
Q9. The
dimensions of a rectangular box are in the ratio 2 : 3: 4 and the difference
between the cost of covering it with sheet of paper at the rate of Rs. 4 and
Rs. 4.50 per square metre is Rs. 416. Find the dimensions of the box.
Q10. The
difference between outside and inside surfaces of a cylindrical metallic pipe
14 cm long is 44 cm2. If the pipe is made of 99 cm3 of
metal, find the outer and inner radii of the pipe ?
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