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    a hemispherical depression is cut from one face of a cubical block, such that diameter l of hemisphere is equal to the edge of cube. find the surface area of the remaining solid.

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    A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

    Click here👆to get an answer to your question ✍️ A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

    Question

    A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

    Medium Open in App

    Updated on : 2022-09-05

    Consider the diagram shown below.

    Solution Verified by Toppr

    It is given that a hemisphere of radius

    2 l ​

    is cut out from the top face of the cuboidal wooden block.

    Therefore, surface area of the remaining solid

    = surface area of the cuboidal box whose each edge is of length l − Area of the top of the hemispherical part + curved surface area of the hemispherical  part

    =6l 2 −πr 2 +2πr 2 =6l 2 −π( 2 l ​ ) 2 +2π( 2 l ​ ) 2 =6l 2 − 4 πl 2 ​ + 2 πl 2 ​ = 4 l 2 ​ (24+π) sq.units

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    A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of remaining solid

    A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. Thus, the surface area of the remaining solid is ¼ l2 (π  + 24).

    A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid

    Solution:

    The figure below of the solid is created as per the given information along with the top view of the solid.

    From the figure, it’s clear that the surface area of the remaining solid includes TSA of the cube, CSA of the hemisphere, and excludes the base of the hemisphere.

    Surface area of the remaining solid = TSA of the cubical part + CSA of the hemispherical part - Area of the base of the hemispherical part

    The remaining area of the solid can be found by using the formulae;

    TSA of the cube = 6 l2, where l is the length of the edge of the cube

    CSA of the hemisphere = 2πr2

    Area of the base of the hemisphere = πr2, where r is the radius of the hemisphere

    Diameter of the hemisphere = Length of the edge of the cube = l

    Radius of the hemisphere, r = l / 2

    Surface area of the remaining solid = TSA of the cubical part + CSA of the hemispherical part - Area of the base of the hemispherical part

    = 6 l2 + 2πr2 - πr2 = 6 l2 + πr2 = 6 l2 + π (l/2)2 = 6 l2 + πl2 / 4 = ¼ l2 (π  + 24)

    Thus, the surface area of the remaining solid is ¼ l2 (π  + 24).

    ☛ Check: NCERT Solutions for Class 10 Maths Chapter 13Video Solution:

    A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid

    NCERT Solutions Class 10 Maths  Chapter 13 Exercise 13.1 Question 5

    Summary:

    The surface area of the remaining solid if a hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube is ¼ l2 (π + 24).

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    स्रोत : www.cuemath.com

    Ex 13.1, 5

    Ex 13.1, 5 A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. Here, diameter of the hemisphere is equal to the edge of the cube So, diame

    Check sibling questions

    Ex 13.1, 5 - Chapter 13 Class 10 Surface Areas and Volumes (Term 2)

    Last updated at Aug. 5, 2021 by Teachoo

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    Transcript

    Ex 13.1, 5 A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. Here, diameter of the hemisphere is equal to the edge of the cube So, diameter = side of cube = l Here, base of hemisphere would not be included in the total solid area of wooden cube . Surface area of solid = Area of cube + Curved surface area of hemisphere Base area of hemisphere Area of cube Here, side = l Area of cube = 6(Side)2 = 6l2 Curved surface area of hemisphere Diameter of hemisphere = l Hence, radius = r = (Diameter )/2 = /2 Curved Surface area of hemisphere = 2 2 = 2 ( /2)^2 =2 ^2/4 = ( ^2)/2 Base area of hemisphere Base of hemisphere is a circle with radius = radius of hemisphere = r = /2 Base area of hemisphere = 2 = ( /2)^2 = ^2/4 = ( ^2)/4 Now, Surface area of solid = Area of cube + Curved surface area of hemisphere Base area of hemisphere = 6l2 + ( ^2)/2 ( ^2)/4 = 6l2 + (2 ^2 ^2)/4 = 6l2 + ( ^2)/4 = l2 (6 + /4) = l2 ((6(4) + )/4) = l2 ((24 + )/4) = 1/4l2 ( + 24) Hence, Surface area of solid = 1/4l2 ( + 24)

    Next: Ex 13.1, 6 →

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