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Surface Areas and Volumes Ex 13.1 Solutions

Question - 1 : -

2 cubes each ofvolume 64 cm3 are joined end to end. Find the surface area ofthe resulting cuboid.

Answer - 1 : -

Question - 2 : -

A vessel is in theform of a hollow hemisphere mounted by a hollow cylinder. The diameter of thehemisphere is 14 cm and the total height of the vessel is 13 cm. Find the innersurface area of the vessel.

Answer - 2 : -

Question - 3 : -

A toy is in the formof a cone of radius 3.5 cm mounted on a hemisphere of same radius. The totalheight of the toy is 15.5 cm. Find the total surface area of the toy.

Answer - 3 : -

Question - 4 : -

A cubical block ofside 7 cm is surmounted by a hemisphere. What is the greatest diameter thehemisphere can have? Find the surface area of the solid.

Answer - 4 : -

Question - 5 : -

A hemisphericaldepression is cut out from one face of a cubical wooden block such that thediameter l of the hemisphere is equal to the edge of the cube. Determine thesurface area of the remaining solid.

Answer - 5 : -

The diagram is as follows:

Now, the diameter of hemisphere = Edge of thecube = l

So, the radius of hemisphere = l/2

∴ The total surface area of solid = surface area of cube + CSA ofhemisphere – Area of base of hemisphere

TSA of remaining solid = 6 (edge)2+2πr2-πr2

= 6l2 πr2

= 6l2+π(l/2)2

= 6l2+πl2/4

= l2/4(24+π) sq. units

Question - 6 : - A medicine capsule is in the shape of acylinder with two hemispheres stuck to each of its ends. The length of theentire capsule is 14 mm and the diameter of the capsule is 5 mm. Find itssurface area.

Answer - 6 : -

Solution

Two hemisphere and one cylinder are shown inthe figure given below.

Here, the diameter of the capsule = 5 mm

∴ Radius = 5/2 = 2.5 mm

Now, the length of the capsule = 14 mm

So, the length of the cylinder = 14-(2.5+2.5)= 9 mm

∴ The surface area of a hemisphere = 2πr2 =2×(22/7)×2.5×2.5

= 275/7 mm2

Now, the surface area of the cylinder = 2πrh

= 2×(22/7)×2.5×9

(22/7)×45 = 990/7 mm2

Thus, the required surface area of medicinecapsule will be

= 2×surface area of hemisphere + surface areaof the cylinder

= (2×275/7) × 990/7

(550/7) + (990/7) = 1540/7 = 220 mm2

Question - 7 : -

A tent is in theshape of a cylinder surmounted by a conical top. If the height and diameter ofthe cylindrical part are 2.1 m and 4 m respectively, and the slant height ofthe top is 2.8 m, find the area of the canvas used for making the tent. Also,find the cost of the canvas of the tent at the rate of Rs 500 per m2.(Note that the base of the tent will not be covered with canvas.)

Answer - 7 : -

Question - 8 : -

From a solidcylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the

same height and samediameter is hollowed out. Find the total surface area of the

remaining solid tothe nearest cm2.

Answer - 8 : -

Question - 9 : -

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, 

Answer - 9 : -

as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article

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