Mensuration 3D - Study Mode

[#51] The curved surface area and volume of a cylindrical object are 88 cm 2 and 132 cm 3 , respectively. The height (in cm) of the cylindrical object is:
Correct Answer

(B) 4$$frac{2}{3}$$

Explanation

Solution: Curved area of cylinder = 88 cm 2 2πrh = 88 2 × $$frac{{22}}{7}$$ × r × h = 88 r × h = 14 Volume of cylinder = πr 2 h = 132 cm 3 $$frac{{22}}{7}$$ × r 2 h = 132 r 2 h = 42 r × rh = 42 r × 14 = 42 r = 3 r × h = 14 h $$ = frac{{14}}{3} = 4frac{2}{3}$$ Height $$ = 4frac{2}{3}{ ext{ cm}}$$

[#52] The ratio of weights of two spheres of different materials is 8 : 17 and the ratio of weights per 1 cc of materials of each is 289 : 64. The ratio of radii of the two spheres is
Correct Answer

(A) 8 : 17

Explanation

Solution: Ratio of volume of sphere × ratio of weight per 1 cc of material of each = Ratio of weight of two sphere $$eqalign{
& frac{{frac{4}{3}pi r_1^3}}{{frac{4}{3}pi r_2^3}} imes frac{{289}}{{64}} = frac{8}{{17}} cr
& frac{{r_1^3}}{{r_2^3}} = frac{{8 imes 64}}{{17 imes 289}} cr
& frac{{{r_1}}}{{{r_2}}} = frac{{8 imes 8 imes 8}}{{17 imes 17 imes 17}} cr
& frac{{{r_1}}}{{{r_2}}} = frac{8}{{17}} cr
& {r_1}:{r_2} = 8:17 cr} $$

[#53] The base of a right prism is a trapezium. The length of the parallel sides are 8 cm and 14 cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm 3 , then the height of the prism is
Correct Answer

(C) 12 cm

Explanation

Solution: Area of trapezium = $$frac{1}{2}$$ × h(AB + CD) = $$frac{1}{2}$$ × 8 × (8 + 14) = 4 × 22 = 88 cm 2 Volume of prism = Height of prism × Area of base ⇒ height × 88 = 1056 (given) ⇒ height = $$frac{{1056}}{{88}}$$ ⇒ height = 12 cm

[#54] Determine the total surface area of a hemisphere closed at bottom. Radius of the hemisphere is $$sqrt {frac{{25}}{pi }} $$ xa0unit.
Correct Answer

(A) 75 unit 2

Explanation

Solution: Total surface area (TSA) of hemisphere = 3πr 2 Radius of hemisphere = $$sqrt {frac{{25}}{pi }} $$ So, TSA = 3 × π × $${left( {sqrt {frac{{25}}{pi }} }
ight)^2}$$ = 75 unit 2

[#55] A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and length is 2 m. How much metal (in cm 3 ) has been used in making the tube?
Correct Answer

(A) 750π

Explanation

Solution: Outer radius = 4 cm Internal radius = 4 - 0.5 = 3.5 cm Length = 2m = 200 cm Volume of cylinder = π × (R 2 - r 2 )h = π × (4 2 - 3.5 2 ) × 200 = π × 7.5 × 0.5 × 200 = 750π